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Littérature scientifique sur le sujet « Abelian varietie »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 10 mars 2023

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Articles de revues sur le sujet "Abelian varietie"

Zhao, Heer. « Degenerating abelian varieties via log abelian varieties ». Asian Journal of Mathematics 22, n^o 5 (2018) : 811–40. http://dx.doi.org/10.4310/ajm.2018.v22.n5.a2.

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Silverberg, Alice. « abelian varieties ». Duke Mathematical Journal 56, n^o 1 (février 1988) : 41–46. http://dx.doi.org/10.1215/s0012-7094-88-05603-7.

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Yu, Chia-Fu. « Abelian varieties over finite fields as basic abelian varieties ». Forum Mathematicum 29, n^o 2 (1 mars 2017) : 489–500. http://dx.doi.org/10.1515/forum-2014-0141.

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AbstractIn this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic ${p>0}$ is isogenous to another one defined over a finite field. We also show that the category of abelian varieties over finite fields up to isogeny can be embedded into the category of basic abelian varieties with suitable endomorphism structures. Using this connection, we derive a new mass formula for a finite orbit of polarized abelian surfaces over a finite field.

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Kajiwara, Takeshi, Kazuya Kato et Chikara Nakayama. « Logarithmic Abelian Varieties ». Nagoya Mathematical Journal 189 (2008) : 63–138. http://dx.doi.org/10.1017/s002776300000951x.

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AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.

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Yamaki, Kazuhiko. « Trace of abelian varieties over function fields and the geometric Bogomolov conjecture ». Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, n^o 741 (1 août 2018) : 133–59. http://dx.doi.org/10.1515/crelle-2015-0086.

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Abstract We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety. To prove the results, we investigate closed subvarieties of abelian schemes over constant varieties, where constant varieties are varieties over a function field which can be defined over the constant field of the function field.

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Totaro, Burt. « Pseudo-abelian varieties ». Annales scientifiques de l'École normale supérieure 46, n^o 5 (2013) : 693–721. http://dx.doi.org/10.24033/asens.2199.

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Ji, Shanyu. « on abelian varieties ». Duke Mathematical Journal 58, n^o 3 (juin 1989) : 657–67. http://dx.doi.org/10.1215/s0012-7094-89-05831-6.

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Bosch, Siegfried, et Werner Lütkebohmert. « Degenerating abelian varieties ». Topology 30, n^o 4 (1991) : 653–98. http://dx.doi.org/10.1016/0040-9383(91)90045-6.

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Archinard, Natália. « Hypergeometric Abelian Varieties ». Canadian Journal of Mathematics 55, n^o 5 (1 octobre 2003) : 897–932. http://dx.doi.org/10.4153/cjm-2003-037-4.

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AbstractIn this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.

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Chai, Ching-Li, et Frans Oort. « Hypersymmetric Abelian Varieties ». Pure and Applied Mathematics Quarterly 2, n^o 1 (2006) : 1–27. http://dx.doi.org/10.4310/pamq.2006.v2.n1.a2.

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Thèses sur le sujet "Abelian varietie"

TAMBORINI, CAROLINA. « On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371476.

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Oggetto di questa tesi sono le sottovarietà totalmente geodetiche dello spazio dei moduli A_g di varietà abeliane principalmente polarizzate e la loro relazione con il luogo di Torelli. Questo è definito come la chiusura in A_g dell'immagine dello spazio dei moduli M_g di curve algebriche complesse lisce di genere g tramite la mappa di Torelli j: M_g-->A_g. Lo spazio dei moduli A_g è un quoziente dello spazio di Siegel, che è uno spazio simmetrico. Una sottovarietà algebrica di A_g è totalmente geodetica se è l'immagine, tramite la naturale mappa di proiezione, di una qualche sottovarietà totalmente geodetica dello spazio di Siegel. Ci si aspetta che j(M_g) contenga poche sottovarietà totalmente geodetiche di A_g. Questo è anche in accordo con la congettura di Coleman-Oort. La geometria differenziale degli spazi simmetrici si può descrivere attraverso la teoria di gruppi e algebre di Lie. In particolare, le sottovarietà totalmente geodetiche di spazi simmetrici possono essere caratterizzate in termini di algebre di Lie. Queste considerazioni sono alla base della trattazione svolta in questa tesi, in cui utilizziamo alcuni strumenti della teoria di Lie per indagare alcuni aspetti geometrici dell'inclusione di j(M_g) in A_g. I principali risultati presentati sono i seguenti. Nel Capitolo 2, consideriamo il pull-back dell'operazione di Lie-bracket sullo spazio tangente ad A_g tramite la mappa di Torelli e lo caratterizziamo in termini della geometria della curva. Per farlo usiamo il nucleo di Bergman associato alla curva. Inoltre, colleghiamo il nucleo di Bergman alla seconda forma fondamentale della mappa Torelli. Nel Capitolo 3, determiniamo quale spazio simmetrico uniforma ciascuno dei controesempi noti alla congettura di Coleman-Oort attraverso il calcolo della decomposizione dell'algebra di Lie associata. Questi esempi noti erano stati ottenuti studiando famiglie di rivestimenti di Galois. Nel capitolo 4 ci concentriamo sullo studio di queste famiglie e descriviamo una nuova costruzione topologica di famiglie di G-rivestimenti di P^1.
This thesis deals with totally geodesic subvarieties of the moduli space A_g of principally polarized abelian varieties and their relation with the Torelli locus. This is the closure in A_g of the image of the moduli space M_g of smooth, complex algebraic curves of genus g via the Torelli map j: M_g-->A_g. The moduli space A_g is a quotient of the Siegel space, which is a Riemannian symmetric space. An algebraic subvariety of A_g is totally geodesic if it is the image, under the natural projection map, of some totally geodesic submanifold of the Siegel space. Geometric considerations lead to the expectation that j(M_g) should contain very few totally geodesic subvarieties of A_g. This expectation also agrees with the Coleman-Oort conjecture. The differential geometry of symmetric spaces is described through Lie theory. In particular, totally geodesic submanifolds can be characterized via Lie algebras. This motivates the discussion carried out in this thesis, in which we use some Lie-theoretic tools to investigate geometric aspects of the inclusion of j(M_g) in A_g. The main results presented are the following. In Chapter 2, we consider the pull-back of the Lie bracket operation on the tangent space of A_g via the Torelli map, and we characterize it in terms of the geometry of the curve. We use the Bergman kernel form associated with the curve. Also, we link the Bergman kernel form to the second fundamental form of the Torelli map. In Chapter 3, we determine which symmetric space uniformizes each of the known counterexamples to the Coleman-Oort conjecture via the computation of the associated Lie algebra decomposition. These known examples were obtained studying families of Galois coverings of curves. Chapter 4 focuses on these families for their own sake, and we describe a new topological construction of families of G-coverings of the line.

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歐偉民 et Wai-man Au. « Families of polarized abelian varieties ». Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31214897.

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Lemos, Pedro. « Residual representations of Abelian varieties ». Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/94788/.

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This thesis is divided in two parts, corresponding to two papers in which I collaborated during the course of my PhD studies. Both of these parts are concerned with the question of surjectivity of residual Galois representations arising from abelian varieties defined over Q. At the start of each chapter, a full introduction to the topic covered is provided.

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Fhlathuin, Brid ni. « Mahler's measure on Abelian varieties ». Thesis, University of East Anglia, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296951.

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This thesis is a study of the integration of proximity functions over certain compact groups. Mean values are found of the ultrametric valuation of certain rational functions associated with a divisor on an abelian variety, and it is shown how these may be expressed in terms of an integral, thus finding the analogue, for an abelian variety, of Mahler's definition of the measure of a polynomial. These integrals are shown to arise in a manner which mimics classical Riemann sums, and their relation with the global canonical height is investigated. It is shown that the measure is a rational multiple of log p. Similar results are given for elliptic curves, taking the divisor to be the identity of the group law, and somewhat stronger mean value theorems proven in this more specific case by working directly with local canonical heights rather than approaching them through related functions. Effective asymptotic formulae for the local height are derived, first for the kernel of reduction of a curve and then, via a detailed analysis of the local reduction of the curve, for the group of rational points. The theory of uniform distribution is used to show that the mean value also takes an integral form in the case of an archimedean valuations, and recent inequalities for elliptic forms in logarithms are used to give error terms for the convergence towards the measure. This is undertaken first for the local height on an elliptic curve, and then, in terms of general theta-functions, on an abelian variety. We then seek to exploit these generalisations of the Mahler measure to yield an alternative method to that of Silverman and Tate for the determining of the global height. The integration over a cyclic group of the laws satisfied locally by the height allows us to reformulate our theorems in a manner conducive to practical application. It is demonstrated how our asymptotic formulae may be used together with an appropriate computer software package, PARI in our case, to calculate the mean value of heights, and, more generally, of rational functions, on an elliptic curve and on abehan varieties of higher genus. Some such calculations are displayed, with comments on their efficacy and their possible future development.

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Au, Wai-man. « Families of polarized abelian varieties / ». Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19471117.

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Young, Ian David. « Symmetric squares of modular Abelian varieties ». Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500087.

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Giangreco, Maidana Alejandro José. « Cyclic abelian varieties over finite fields ». Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0316.

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L'ensemble A(k) des points rationnels d'une variété abélienne A définie sur un corps fini k forme un groupe abélien fini. Ce groupe convient pour des multiples applications, et sa structure est très importante. Connaître les possibles structures de groupe des A(k) et quelques statistiques est donc fondamental. Dans cette thèse, on s'intéresse aux "variétés cycliques", i.e. variétés abéliennes définies sur des corps finis avec groupe des points rationnels cyclique.Les isogénies nous donnent une classification plus grossière que celle donnée par les classes d'isomorphisme des variétés abéliennes, mais elles offrent un outil très puissant en géométrie algébrique. Chaque classe d'isogénie est déterminée par son polynôme de Weil. On donne un critère pour caractériser les "classes d'isogénies cycliques", i.e. classes d'isogénies de variétés abéliennes définies sur des corps finis qui contiennent seulement des variétés cycliques. Ce critère est basé sur le polynôme de Weil de la classe d'isogénie.À partir de cela, on donne des bornes de la proportion de classes d'isogénies cycliques parmi certaines familles de classes d'isogénies paramétrées par ses polynômes de Weil.On donne aussi la proportion de classes d'isogénies cycliques "locaux" parmi les classes d'isogénie définies sur des corps finis mathbb{F}_q avec q éléments, quand q tend à l'infini
The set A(k) of rational points of an abelian variety A defined over a finite field k forms a finite abelian group. This group is suitable for multiple applications, and its structure is very important. Knowing the possible group structures of A(k) and some statistics is then fundamental. In this thesis, we focus our interest in "cyclic varieties", i.e. abelian varieties defined over finite fields with cyclic group of rational points. Isogenies give us a coarser classification than that given by the isomorphism classes of abelian varieties, but they provide a powerful tool in algebraic geometry. Every isogeny class is determined by its Weil polynomial. We give a criterion to characterize "cyclic isogeny classes", i.e. isogeny classes of abelian varieties defined over finite fields containing only cyclic varieties. This criterion is based on the Weil polynomial of the isogeny class.From this, we give bounds on the fractions of cyclic isogeny classes among certain families of isogeny classes parameterized by their Weil polynomials.Also we give the proportion of "local"-cyclic isogeny classes among the isogeny classes defined over the finite field mathbb{F}_q with q elements, when q tends to infinity

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Joyce, Adam Jack. « The Manin constants of modular abelian varieties ». Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440468.

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Lahoz, Vilalta Marti. « Theta-duality in abelian varieties and the bicanonical map of irregular varieties ». Doctoral thesis, Universitat Politècnica de Catalunya, 2010. http://hdl.handle.net/10803/77898.

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The first goal of this Thesis is to contribute to the study of principally polarized abelian varieties (ppav), especially to the Schottky and the Torelli problems. Ppav admit a duality theory analogous to that of projective spaces, where the role played by hyperplanes in projective spaces is played by divisors representing the principal polarization. Thus, given a subvariety Y of a ppav, we can define its thetadual T(Y) as the set of divisors representing the principal polarization that contain this subvariety. This set admits a natural schematic structure (as defined by Pareschi and Popa). Jacobian and Prym varieties are classical examples of ppav constructed from curves. Besides, they are interesting because some properties of the curves involved in their construction are reflected in their geometry or in the geometry of some special subvarieties. For example, in the case of Jacobians we have the BrillNoether loci Wd ( W1 corresponds to the AbelJacobi curve) and in the case of Pryms we have the AbelPrym curve C. In chapter III, we study the schematic structure of the thetadual of the BrillNoether loci Wd and the AbelPrym curve. In the first case, we obtain with different methods, the result of Pareschi and Popa T(Wd)= Wgd1. In the case of the AbelPrym curve C, we get that T(C)=V², where V² is the second PrymBrillNoether locus with the schematic structure defined by Welters. Pareschi and Popa have proved a result for ppavs analogous to the Castelnuovo Lemma for projective spaces. That is, if (A,Θ) is a ppav of dimension g, then g+2 distinct points in general position with respect to Θ, but in special position with respect to 2Θ, have to be contained in a curve of minimal degree in A, i.e. an AbelJacobi curve. In particular, they obtain a Schottky result because A has to be a Jacobian variety and a Torelli result, because the curve is the intersection of all the divisors in |2Θ| that contain the g+2 points. In chapter IV, as Eisenbud and Harris have done in the projective Castelnuovo Lemma, we extend this result to possibly nonreduced finite schemes. The second goal of this thesis is the study of varieties of general type. Almost by definition, pluricanonical maps are the essential tool to study them. One of the main problems in this area is to find geometric or numerical conditions to guarantee that the mth pluricanonical map (for low m) induces a birational equivalence with its image. The classification of surfaces whose bicanonical map is nonbirational has attracted considerable interest among algebraic geometers. In chapter V, we give a sufficient numerical condition for the birationality of the bicanonical map of irregular varieties of arbitrary dimension. We also prove that, if X is a primitive variety, then it only admits very special fibrations to other irregular varieties. For primitive varieties we get that the following are equivalent: X is birational to a divisor Θ in an indecomposable ppav, the irregularity q(X) > dim X and the bicanonical map is nonbirational. When X is a primitive variety of general type and q(X) = dim X we prove, under certain conditions over the Stein factorization of the Albanese map, that the only possibility for the bicanonical map being nonbirational is that X is a double cover branched along a divisor in |2Θ|. These results extend to arbitrary dimension, wellknown theorems in the case of surfaces and curves.
El primer objectiu d'aquesta tesi és contribuir a l'estudi de les varietats abelianes principalment polaritzades (vapp), especialment als problemes de Schottky i Torelli. Les vapp admeten una teoria de dualitat anàloga a la dualitat dels espais projectius, on el paper que juguen els hiperplans de l'espai projectiu és substituït pels divisors que representen la polarització principal. Així doncs, donada una subvarietat Y d'una vapp, podem definir el seu thetadual T(Y) com el conjunt dels divisors que representen la polarització principal i contenen aquesta subvarietat. Aquest conjunt admet una estructura esquemàtica natural (tal i com la defineixen Pareschi i Popa). Les varietats Jacobianes i de Prym són exemples clàssics de vapp construïdes a partir de corbes. A més, són interessants perquè certes propietats de les corbes involucrades es veuen reflectides en elles o en algunes subvarietats especials. Per exemple, en el cas de les Jacobianes tenim els llocs de BrillNoether Wd ( W1 correspon a la corba d'AbelJacobi) i en el cas de les Pryms tenim la corba d'AbelPrym C. Al capítol III de la tesi s'estudia l'estructura esquemàtica del thetadual dels llocs de BrillNoether Wd i de la corba d'AbelPrym. En el primer cas, es reobté amb uns altres mètodes, el resultat de Pareschi i Popa T(Wd)= Wgd1. En el cas de la corba d'AbelPrym C, s'obté que T(C)=V², onV² és el segon lloc de PrymBrillNoether amb l'estructura esquemàtica definida per Welters. Pareschi i Popa han demostrat un resultat anàleg per les vapp al Lemma de Castelnuovo pels espais projectius. És a dir, si (A,Θ) és una vapp de dimensió g, aleshores g+2 punts en posició general respecte Θ, però en posició especial respecte 2Θ, han d'estar continguts en una corba de grau minimal a A, i.e. una corba d'AbelJacobi. En particular, s'obté un resultat de Schottky ja que A ha de ser una Jacobiana i un resultat de Torelli, ja que la corba és la intersecció de tots els divisors de |2Θ| que contenen els g+2 punts. Al capítol IV, tal i com Eisenbud i Harris van fer en el cas projectiu, s'estén aquest resultat a esquemes finits possiblement no reduïts. El segon objectiu d'aquesta tesi és contribuir a l'estudi de les varietats de tipus general. Pràcticament per definició, les aplicacions pluricanòniques són essencials pel seu estudi. Un dels problemes principals de l'àrea és donar condicions geomètriques o numèriques per assegurar que la mèsima aplicació pluricanònica (per m baix) indueix una equivalència biracional amb la imatge. La classificació de les superfícies que tenen l'aplicació bicanònica no biracional ha atret l'atenció de molts geòmetres algebraics. Al capítol V, es dóna un criteri numèric suficient per assegurar la biracionalitat de l'aplicació bicanònica de les varietats irregulars de dimensió arbitrària. També es demostra que si X és una varietat primitiva, aleshores només admet fibracions molt especials a altres varietats irregulars. Per aquestes varietats s'obté que és equivalent que X sigui biracional a un divisor Θ en una vapp indescomponible, a què la irregularitat q(X) > dim X i l'aplicació bicanònica sigui no biracional. Quan X és una varietat primitiva de tipus general i q(X) = dim X es demostra sota certes condicions de la descomposició de Stein del morfisme d'Albanese, que l'única possibilitat per tal que l'aplicació bicanònica sigui no biracional és que X sigui un recobriment doble sobre una vapp ramificat al llarg d'un divisor a |2Θ|. Aquest resultats estenen a dimensió arbitrària, teoremes ben coneguts en el cas de superfícies i corbes.

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Borowka, Pawel. « Non-simple abelian varieties and (1,3) Theta divisors ». Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.564009.

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This thesis studies non-simple Jacobians and non-simple abelian varieties. The moti- vation of the study is a construction which gives a distinguished genus 4 curve in the linear system of a (1, 3)-polarised surface. The main theorem characterises such curves as hyperelliptic genus 4 curves whose Jacobian contains a (1, 3)-polarised surface. This leads to investigating the locus of non-simple principally polarised abelian g- folds. The main theorem of this part shows that the irreducible components of this locus are Is~, defined as the locus of principally polarised g-folds having an abelian subvariety with induced polarisation of type d. = (d1, ... , dk), where k ≤ g/2 Moreover, there are theorems which characterise the Jacobians of curves that are etale double covers or double covers branched in two points. There is also a detailed computation showing that, for p > 1 an odd number, the hyperelliptic locus meets IS4(l,p) transversely in the Siegel upper half space

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Livres sur le sujet "Abelian varietie"

Barth, Wolf, Klaus Hulek et Herbert Lange, dir. Abelian Varieties. Berlin, New York : DE GRUYTER, 1995. http://dx.doi.org/10.1515/9783110889437.

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Lange, Herbert. Complex Abelian varieties. Berlin : Springer, 1992.

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Lange, Herbert, et Christina Birkenhake. Complex Abelian Varieties. Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2.

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Birkenhake, Christina, et Herbert Lange. Complex Abelian Varieties. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1.

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H, Lange. Complex Abelian varieties. Berlin : Springer-Verlag, 1992.

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1943-, Lange H., et Lange H. 1943-, dir. Complex Abelian varieties. 2^e éd. Berlin : Springer, 2004.

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Faber, Carel, Gerard van der Geer et Frans Oort, dir. Moduli of Abelian Varieties. Basel : Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0.

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Faltings, Gerd, et Ching-Li Chai. Degeneration of Abelian Varieties. Berlin, Heidelberg : Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-02632-8.

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Adler, Allan, et Sundararaman Ramanan. Moduli of Abelian Varieties. Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0093659.

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Alexeev, Valery, Arnaud Beauville, C. Herbert Clemens et Elham Izadi, dir. Curves and Abelian Varieties. Providence, Rhode Island : American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/465.

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Chapitres de livres sur le sujet "Abelian varietie"

Gamkrelidze, R. V. « Abelian Varieties ». Dans Encyclopaedia of Mathematical Sciences, 68–100. Berlin, Heidelberg : Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58227-1_3.

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Fresnel, Jean, et Marius van der Put. « Abelian Varieties ». Dans Rigid Analytic Geometry and Its Applications, 165–89. Boston, MA : Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0041-3_6.

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Milne, J. S. « Abelian Varieties ». Dans Arithmetic Geometry, 103–50. New York, NY : Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_5.

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Hurt, Norman E. « Abelian Varieties ». Dans Many Rational Points, 1–126. Dordrecht : Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0251-5_1.

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Birkenhake, Christina, et Herbert Lange. « Abelian Varieties ». Dans Complex Abelian Varieties, 69–112. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_6.

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Lange, Herbert, et Christina Birkenhake. « Abelian Varieties ». Dans Complex Abelian Varieties, 71–114. Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_6.

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Birkenhake, Christina, et Herbert Lange. « Jacobian Varieties ». Dans Complex Abelian Varieties, 315–62. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_13.

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Birkenhake, Christina, et Herbert Lange. « Prym Varieties ». Dans Complex Abelian Varieties, 363–409. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_14.

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Lange, Herbert, et Christina Birkenhake. « Jacobian Varieties ». Dans Complex Abelian Varieties, 320–64. Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_13.

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Lange, Herbert, et Christina Birkenhake. « Prym Varieties ». Dans Complex Abelian Varieties, 365–408. Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_14.

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Actes de conférences sur le sujet "Abelian varietie"

Blake, Ian F. « Abelian varieties in coding and cryptography ». Dans 2010 IEEE Information Theory Workshop (ITW 2010). IEEE, 2010. http://dx.doi.org/10.1109/cig.2010.5592929.

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Lawson, Tyler. « An overview of abelian varieties in homotopy theory ». Dans New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.179.

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POLÁK, L. « LITERAL VARIETIES AND PSEUDOVARIETIES OF HOMOMORPHISMS ONTO ABELIAN GROUPS ». Dans Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708700_0018.

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