Relevant bibliographies by topics / Ramification bounds

Academic literature on the topic 'Ramification bounds'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Ramification bounds"

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Garza, John. "The Lehmer strength bounds for total ramification." Acta Arithmetica 137, no. 2 (2009): 171–76. http://dx.doi.org/10.4064/aa137-2-5.

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Zak, F. L. "Castelnuovo bounds for higher-dimensional varieties." Compositio Mathematica 148, no. 4 (July 2012): 1085–132. http://dx.doi.org/10.1112/s0010437x1100738x.

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AbstractWe give bounds for the Betti numbers of projective algebraic varieties in terms of their classes (degrees of dual varieties of successive hyperplane sections). We also give bounds for classes in terms of ramification volumes (mixed ramification degrees), sectional genus and, eventually, in terms of dimension, codimension and degree. For varieties whose degree is large with respect to codimension, we give sharp bounds for the above invariants and classify the varieties on the boundary, thus obtaining a generalization of Castelnuovo’s theory for curves to varieties of higher dimension.
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Bary-Soroker, Lior, and Tomer M. Schlank. "SIEVES AND THE MINIMAL RAMIFICATION PROBLEM." Journal of the Institute of Mathematics of Jussieu 19, no. 3 (June 18, 2018): 919–45. http://dx.doi.org/10.1017/s1474748018000257.

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The minimal ramification problem may be considered as a quantitative version of the inverse Galois problem. For a nontrivial finite group $G$, let $m(G)$ be the minimal integer $m$ for which there exists a $G$-Galois extension $N/\mathbb{Q}$ that is ramified at exactly $m$ primes (including the infinite one). So, the problem is to compute or to bound $m(G)$.In this paper, we bound the ramification of extensions $N/\mathbb{Q}$ obtained as a specialization of a branched covering $\unicode[STIX]{x1D719}:C\rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$. This leads to novel upper bounds on $m(G)$, for finite groups $G$ that are realizable as the Galois group of a branched covering. Some instances of our general results are: $$\begin{eqnarray}1\leqslant m(S_{k})\leqslant 4\quad \text{and}\quad n\leqslant m(S_{k}^{n})\leqslant n+4,\end{eqnarray}$$ for all $n,k>0$. Here $S_{k}$ denotes the symmetric group on $k$ letters, and $S_{k}^{n}$ is the direct product of $n$ copies of $S_{k}$. We also get the correct asymptotic of $m(G^{n})$, as $n\rightarrow \infty$ for a certain class of groups $G$.Our methods are based on sieve theory results, in particular on the Green–Tao–Ziegler theorem on prime values of linear forms in two variables, on the theory of specialization in arithmetic geometry, and on finite group theory.
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Caruso, Xavier, and Tong Liu. "Some bounds for ramification of pn-torsion semi-stable representations." Journal of Algebra 325, no. 1 (January 2011): 70–96. http://dx.doi.org/10.1016/j.jalgebra.2010.10.005.

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BRUEGGEMAN, SHARON, and DARRIN DOUD. "LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS." International Journal of Number Theory 04, no. 03 (June 2008): 349–61. http://dx.doi.org/10.1142/s1793042108001389.

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Using analytic techniques of Odlyzko and Poitou, we create tables of lower bounds for discriminants of number fields, including local corrections for ideals of known norm. Comparing the lower bounds found in these tables with upper bounds on discriminants of number fields obtained from calculations involving differents, we prove the nonexistence of a number of small degree extensions of quadratic fields having limited ramification. We note that several of our results require the locally corrected bounds.
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LOZANO-ROBLEDO, ÁLVARO, and BENJAMIN LUNDELL. "BOUNDS FOR THE TORSION OF ELLIPTIC CURVES OVER EXTENSIONS WITH BOUNDED RAMIFICATION." International Journal of Number Theory 06, no. 06 (September 2010): 1293–309. http://dx.doi.org/10.1142/s1793042110003514.

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Let E be a semi-stable elliptic curve defined over ℚ, and fix N ≥ 2. Let KN/ℚ be a maximal algebraic Galois extension of ℚ whose ramification indices are all at most N. We show that there exists a computable bound B(N), which depends only on N and not on the choice of E/ℚ, such that the size of E(KN) Tors is always at most B(N).
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Jones, John W. "Wild ramification bounds and simple group Galois extensions ramified only at $2$." Proceedings of the American Mathematical Society 139, no. 03 (March 1, 2011): 807. http://dx.doi.org/10.1090/s0002-9939-2010-10628-7.

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Assim, J., and A. Movahhedi. "Norm index formula for the Tate kernels and applications." Journal of K-Theory 9, no. 2 (May 24, 2011): 359–83. http://dx.doi.org/10.1017/is011003006jkt135.

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AbstractLet p be an odd prime and L/F a p-extension of number fields with Galois group G. The aim of this paper is to provide answers to a question of Kahn concerning lower bounds for the order of the kernel and cokernel of the functorial map K2F → K2LG. To this end, we first determine a norm index formula for generalized Tate kernels and then express our lower bounds in terms of the ramification in L/F.
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Clark, Pete L., and Xavier Xarles. "Local Bounds for Torsion Points on Abelian Varieties." Canadian Journal of Mathematics 60, no. 3 (June 1, 2008): 532–55. http://dx.doi.org/10.4153/cjm-2008-026-x.

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AbstractWe say that an abelian variety over a p-adic field K has anisotropic reduction (AR) if the special fiber of its Néronminimal model does not contain a nontrivial split torus. This includes all abelian varieties with potentially good reduction and, in particular, those with complex or quaternionic multiplication. We give a bound for the size of the K-rational torsion subgroup of a g-dimensional AR variety depending only on g and the numerical invariants of K (the absolute ramification index and the cardinality of the residue field). Applying these bounds to abelian varieties over a number field with everywhere locally anisotropic reduction, we get bounds which, as a function of g, are close to optimal. In particular, we determine the possible cardinalities of the torsion subgroup of an AR abelian surface over the rational numbers, up to a set of 11 values which are not known to occur. The largest such value is 72.
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Kramer-Miller, Joe. "The monodromy of unit-root F-isocrystals with geometric origin." Compositio Mathematica 158, no. 2 (February 2022): 334–65. http://dx.doi.org/10.1112/s0010437x2200728x.

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Let $C$ be a smooth curve over a finite field of characteristic $p$ and let $M$ be an overconvergent $\mathbf {F}$ -isocrystal over $C$ . After replacing $C$ with a dense open subset, $M$ obtains a slope filtration. This is a purely $p$ -adic phenomenon; there is no counterpart in the theory of lisse $\ell$ -adic sheaves. The graded pieces of this slope filtration correspond to lisse $p$ -adic sheaves, which we call geometric. Geometric lisse $p$ -adic sheaves are mysterious, as there is no $\ell$ -adic analogue. In this article, we study the monodromy of geometric lisse $p$ -adic sheaves with rank one. More precisely, we prove exponential bounds on their ramification breaks. When the generic slopes of $M$ are integers, we show that the local ramification breaks satisfy a certain type of periodicity. The crux of the proof is the theory of $\mathbf {F}$ -isocrystals with log-decay. We prove a monodromy theorem for these $\mathbf {F}$ -isocrystals, as well as a theorem relating the slopes of $M$ to the rate of log-decay of the slope filtration. As a consequence of these methods, we provide a new proof of the Drinfeld–Kedlaya theorem for irreducible $\mathbf {F}$ -isocrystals on curves.
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Dissertations / Theses on the topic "Ramification bounds"

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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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Books on the topic "Ramification bounds"

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I, Arnolʹd V. Experimental mathematics. Berkeley, California: MSRI Mathematical Sciences Research Institute, 2015.

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Carter, J. Adam, Andy Clark, Jesper Kallestrup, S. Orestis Palermos, and Duncan Pritchard. Extended Epistemology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198769811.003.0001.

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First, a theoretical background to the volume’s topic, extended epistemology, is provided by a brief outline of its cross-disciplinary theoretical lineage and some key themes. In particular, it is shown how and why the emergence of recent and more egalitarian thinking in the cognitive sciences about the nature of human cognizing and its bounds—viz., the so-called ‘extended cognition’ program, and the related idea of an ‘extended mind’—has important and interesting ramifications in epistemology. Second, an overview is provided of the papers included as chapters in the volume. The sixteen contributions are divided (broadly) into two categories: those that engage with foundational issues to do with extended epistemology, and those that pursue applications of extended epistemology to new areas of research.
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Carter, J. Adam, and Jesper Kallestrup. Extended Circularity: A New Puzzle for Extended Cognition. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198769811.003.0003.

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Mainstream epistemology has typically presumed a traditional picture of the metaphysics of mind, whereby cognitive processes (e.g., memory storage and retrieval) play out within the bounds of skull and skin. Contemporary thinking in the philosophy of mind and cognitive science decreasingly favors this simple “intracranial” picture. Likewise, proponents of active externalist approaches to the mind—e.g., the hypothesis of extended cognition (HEC)—have largely proceeded without asking what epistemological ramifications should arise once cognition is understood as criss-crossing between brain and world. This chapter aims to motivate a puzzle that arises once these thought strands are juxtaposed, and highlights a condition of epistemological adequacy that should be accepted by proponents of extended cognition. Once this condition is motivated, the chapter demonstrates how attempts to satisfy it apparently inevitably devolve into a novel epistemic circularity. Eventually, proponents of extended cognition have a novel epistemological puzzle on their hands.
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Fortescue, Michael. What are the Limits of Polysynthesis? Edited by Michael Fortescue, Marianne Mithun, and Nicholas Evans. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199683208.013.14.

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Of the various labels for morphological types currently in use by typologists ‘polysynthesis’ has proved to be the most difficult to pin down. For some it just represents an extreme on the dimension of synthesis (one of Sapir’s two major typological axes), while for others it is an independent category or parameter involving incorporation and bound pronominals with far-reaching morphosyntactic ramifications. If the nub of polysynthesis is the packing of a lot of material into single verb forms that would be expressed as independent words in less synthetic languages, what exactly is the nature of and limitations on this ‘material’? This chapter investigates the limits—both upwards and downwards—of what the term is generally understood to cover and suggests a rule-of-thumb definition. Cognitive constraints on its maximal extent are also considered.
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Weinrib, Jacob. Sovereignty as a Right and as a Duty. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190922542.003.0003.

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The organizing principle of Immanuel Kant’s political philosophy is that each person has a basic right to equal freedom. This principle poses a challenge to the very possibility and purpose of sovereignty. It poses a challenge for the possibility of sovereignty because that idea divides persons into rulers and ruled and empowers the former to change the normative situation of the latter by conferring rights, powers, and immunities, or even imposing coercible obligations. But if each person has a right to equal freedom, how could sovereignty—with its attendant division of persons into ruler and ruled—be possible? Kant’s answer is that sovereignty is possible because it is constitutive of the condition in which private persons interact with one another on terms of equal freedom. Such an approach gives Kant resources both to explain how sovereignty can be justified to those bound by it and to deny that every organization that has a monopoly on violence exercises sovereignty. The right to equal freedom also has significant ramifications for thinking about the kinds of purposes that sovereign power may serve. Implicit in the justification of the sovereign’s right to exercise public authority is an overarching duty to bring the legal order as a whole into the deepest possible conformity with its own animating principle, equal freedom. Thus, Kant’s account of how sovereignty is possible culminates in an account of the duty that accompanies its exercise.
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Book chapters on the topic "Ramification bounds"

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Nowak-Far, Artur. "The Rule of Law Framework in the European Union: Its Rationale, Origins, Role and International Ramifications." In Defending Checks and Balances in EU Member States, 305–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62317-6_12.

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AbstractAt present, the European rule of law enforcement framework under Article 7 TEU (RLF) is vulnerable to unguaranteed, discretionary influences of the Member States. This vulnerability arises from its procedural format which requires high thresholds in decision-making with the effect that this procedure is prone to be terminated by the EU Member States likely to be scrutinized under it, if only they collude. Yet, the Framework may prove effective to correct serious breaches against human rights (in the context of ineffective rule of law standards). The European Commission is bound to pursue the RLF effectiveness for the sake of achieving relative uniformity of application of EU law (at large), and making the European Union a credible actor and co-creator of international legal order. The RLF is an important tool for the maintenance of relative stability of human rights and the rule of law in the EU despite natural divergence propensity resulting from the procedural autonomy of the EU Member States. By achieving this stability, the EU achieves significant political weight in international dialogue concerning human rights and the rule of law and preserves a high level of its global credibility in this context. Thus, RLF increases the EU’s effectiveness in promoting the European model of their identification and enforcement.
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Dorr, Cian, John Hawthorne, and Juhani Yli-Vakkuri. "Alternatives and Challenges." In The Bounds of Possibility, 307–26. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192846655.003.0014.

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After an opening section surveying some possible alternative ways of employing semantic plasticity to handle the puzzles, this chapter discusses two challenges to the view developed in chapters 11 and 12. One involves the threat of rampant error in counterfactual speech reports. The second involves certain uncomfortable consequences of applying our favoured treatment of words like ‘that’ and ‘table’ to words like ‘I’, ‘you’, ‘person’, ‘thinker’, and ‘conscious’. We show how considerations of semantic plasticity militate in the direction of a kind of “metaphysical misanthropy”, and explore its ethical ramifications.
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Gintis, Herbert. "Rationalizability and Common Knowledge of Rationality." In The Bounds of Reason. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691160849.003.0004.

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This chapter deals with the implications of rationality in normal form games. It first explores the ramifications of the rationalizability assumption and shows that in many cases rational individuals will not play rationalizable strategies. It argues that the informal reasoning supporting rationalizability must be replaced by a more rigorous analytical framework. This framework is known as epistemic game theory. Using epistemic game theory, it presents the argument that not rationality, but rather common knowledge of rationality, implies that players will only use rationalizable strategies. The chapter concludes by showing that there is no justification of the common knowledge of rationality assumption, and hence there is no reason to believe that in general rational players will choose rationalizable strategies. It strengthens this conclusion by showing that even assuming common knowledge of rationality, there is no reason for a rational player to conform to the iterated elimination of strongly dominated strategies.
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Zamir, Eyal, and Doron Teichman. "Tort Law." In Behavioral Law and Economics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190901349.003.0010.

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This chapter presents an overview of the behavioral analysis of tort law. It begins by presenting a summary of traditional economic analysis of tort law. That done, it examines various tort regimes (i.e., negligence and strict liability), as well as alternative legal regimes that base liability on the creation of risk rather than the materialization of harm, in light of the bounded rationality of potential tortfeasors and adjudicators. The chapter further explores the implications of behavioral findings for the calculation of damages in tort cases. Finally, it addresses the topic of product liability law, and highlights the ramifications of consumers’ bounded rationality for this area of law.
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Zamir, Eyal, and Doron Teichman. "Commercial Law: Corporate Law, Securities Regulation, and Antitrust." In Behavioral Law and Economics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190901349.003.0011.

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This chapter critically surveys the behavioral analysis of commercial law. It begins by examining the preliminary question of whether bounded rationality can persist in well-functioning, highly competitive markets. As the theoretical analysis and empirical evidence demonstrate, irrational behavior is present even in such settings. The chapter goes on to discuss the implications of behavioral analysis for key issues within corporate law, securities regulation, and antitrust law. These include the ramifications of managers’ overconfidence and passive boards; the bounded rationality of retail investors; and the effect of behavioral phenomena on market competition. The chapter concludes with discussion of the critiques leveled against the behavioral analysis of commercial law.
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Tuszewicki, Marek. "Demons and Witches." In A Frog Under the Tongue, 233–62. Liverpool University Press, 2021. http://dx.doi.org/10.3828/liverpool/9781906764982.003.0013.

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This chapter talks about demons and witches. People believed that an illness or other health issue could be the work of supernatural beings such as demons, devils, or witches. These creatures were thought to do their mischief not by directly entering the victim's body, but usually by using magic. In the popular imagination, humans were constantly surrounded by demons and the like, though not all of these creatures drew satisfaction from making mischief. Ghosts and demons were thought to inhabit specific places, or to be in the habit of behaving in particular ways, and, left in peace, they would not interfere in human affairs. In the folk consciousness, any interference in a sphere perceived to be the domain of unclean forces was bound to render the meddler vulnerable to a more or less violent reaction on the part of those forces. The practical ramifications of this belief were visible in superstitions surrounding matters such as building and moving into a house. Places considered holy and which were reserved for the enactment of rites and rituals were by no means out of bounds to incorporeal beings. There is also a belief there were demons who, at the request of the rebbe, would protect the Jewish community from the local squire's insatiable greed. Almost every type of demon could be persuaded to help humans, and whether or not one was successful in this mission depended chiefly on one's cunning. Nonetheless, the dominant trope in folk tales is of demons harming or causing damage to humans, and even bringing death on them.
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Moran, Ricki L., Cristina Marquez, and James Garner. "Developing Credibility and Establishing Trust." In The Art of Becoming Indispensable, 97–106. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197585160.003.0010.

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This chapter discusses the importance of clearly establishing social worker roles within and outside of the building and the professional ramifications of differential training between school social workers and teachers. Steps are outlined for maintaining the social work code of ethics while partnering with other school personnel who are not bound to the same code. The importance of explaining confidentiality and its limitations early in the professional relationship is stressed. The social worker should remember to self-disclose only when it benefits the client. Advice is offered for building a solid foundation of trust and establishing credibility during a school social worker’s first three years in a school setting. Potential pitfalls will be discussed as well.
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"enterprises are bound to gravitate towards the big cities and the need for marketed surplus beyond that obtainable from the state farms would re-inforce the already existent pattern of extreme concentration of modern inputs in the few agriculturally developed regions of the country. Fourth, it is unlikely to generate the order of urban employment that is required over the plan period. This failure has various ramifications. For one, un-employment would probably become increasingly worse in the smaller towns or else, the migration into the prime cities from other smaller urban centres would increase without, of course, affecting the overall employment outcome. For another, this would mean an exacerbatian of the social costs of such urbanisation, manifest in the forms of an expanding urban lumpenproletariat, prostitution, and begging. Clearly, none of these phenomena should have an extended life in a socialist system. Furthermore, such unemployment would undermine the utility of the rationing system which would fail to reach this needy class on account of their exchange entitlement failure. To meet the distributional objectives, therefore, it would become necessary to rely increasingly on institutional devices of income sharing as a strategic rather than purely tactical option. Case C: An Alternative This offers an alternative strategic framework for a revised DTYP. The central principle underlying this concerns what is adopted as a trinity of objectives, namely, growth, distributional equity, and grassroots participating institutions. The earlier cases are crucially dependent upon an extended circular flow of investible resources extracted from agriculture and invested in industry and related sectors in the form of large projects. This involves little direct participation on the part of the savers and investments occur largely outside the units or sectors from which resources are extracted. Inevitably, aggregate domestic investments would depend upon the open and hidden contributions of peasant agriculture which would also remain a net contributor or loser in resource terms. It is arguable that this type of investment process is unsuited to an economy like Ethiopia where the level of available investible surplus is low and scattered in small denominations, where the degree of economic fragmentation is extreme, and where even the relatively well-developed centre is unlikely to be able to bear the burden imposed upon it. In addition, this strategy is unmindful of harnessing for productive purposes those investible rural resources which are not extractable and therefore not useable through the centralised and dichotomous investment process mentioned above. The collective framework, that is, Case C, takes the relative emphasis away from major industrial investments and places it on investments within the rural sector. The industrial shift involves the locational, size, product and technology dimensions, making the sector less import-intensive and more labour-intensive. Thus, even if the scale of investment was to be lowered, there might be few net losses (in GDP terms) to output, and perhaps even a net gain in terms of intermediate-level skill creation, as well as in direct and indirect employment generated. This would ease the urban poverty." In The Agrarian Question in Socialist Transitions, 181–82. Routledge, 2013. http://dx.doi.org/10.4324/9780203043493-23.

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Conference papers on the topic "Ramification bounds"

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KAWAMURA, TOMOMI. "LOWER BOUNDS FOR THE UNKNOTTING NUMBERS OF THE KNOTS OBTAINED FROM CERTAIN LINKS." In Proceedings of the International Conference on Knot Theory and Its Ramifications. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792679_0013.

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Reports on the topic "Ramification bounds"

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Bain, Rachel, David Young, Marin Kress, Katherine Chambers, and Brandan Scully. US port connectivity and ramifications for maintenance of South Atlantic Division ports. Engineer Research and Development Center (U.S.), January 2023. http://dx.doi.org/10.21079/11681/46385.

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This study utilized automatic identification system (AIS) data to quantify vessel traffic patterns within a predominantly US port network from 1 January 2009 to 31 December 2020, with the methods validated using independent data sets collected between 1 January 2015 and 31 December 2019. The analysis focused on South Atlantic Division (SAD) ports. AIS-derived data characterized individual ports’ traffic and port-to-port connectivity for the network. With foreign vessel entrances and clearances (E&C) data, the AIS-reported vessel characteristics enabled calculation of ships’ physical volume, which was a reasonable proxy for tonnage at many SAD ports. The PageRank algorithm was then applied to port-to-port traffic, revealing how individual ports participate in cargo movement through the network. PageRank scores also provided insight into the maritime supply chain beyond traditional traffic metrics. For example, many East Coast SAD ports ranked higher by PageRank than by raw tonnage. Because of the supply chain implications of shared vessel traffic, PageRank scores can augment tonnage metrics when prioritizing channel and infrastructure maintenance. Vessel volume, port-to-port connectivity, and PageRank scores reveal maritime supply chain resilience by identifying alternative destinations for cargo bound for disrupted ports, robustness across supply chains, and the effects of seasonality and disruptions.
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