Relevant bibliographies by topics / Bloch-Kato conjecture

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Bloch-Kato conjecture'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Bloch-Kato conjecture"

1

Huber, Annette, and Guido Kings. "A cohomological Tamagawa number formula." Nagoya Mathematical Journal 202 (June 2011): 45–75. http://dx.doi.org/10.1215/00277630-1260441.

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AbstractFor smooth linear group schemes over ℤ, we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that in the case of tori, the cohomological and the motivic Tamagawa measures coincide, which proves again the Bloch-Kato conjecture for motives associated to tori.
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Huber, Annette, and Guido Kings. "A cohomological Tamagawa number formula." Nagoya Mathematical Journal 202 (June 2011): 45–75. http://dx.doi.org/10.1017/s0027763000010242.

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AbstractFor smooth linear group schemes over ℤ, we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that in the case of tori, the cohomological and the motivic Tamagawa measures coincide, which proves again the Bloch-Kato conjecture for motives associated to tori.
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3

Swinnerton-Dyer, Sir Peter. "Diagonal hypersurfaces and the Bloch-Kato conjecture, I." Journal of the London Mathematical Society 90, no. 3 (2014): 845–60. http://dx.doi.org/10.1112/jlms/jdu055.

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4

Guo, Li. "On the Bloch–Kato Conjecture for HeckeL-Functions." Journal of Number Theory 57, no. 2 (1996): 340–65. http://dx.doi.org/10.1006/jnth.1996.0053.

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Asok, Aravind. "Rationality problems and conjectures of Milnor and Bloch–Kato." Compositio Mathematica 149, no. 8 (2013): 1312–26. http://dx.doi.org/10.1112/s0010437x13007021.

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AbstractWe show how the techniques of Voevodsky’s proof of the Milnor conjecture and the Voevodsky–Rost proof of its generalization the Bloch–Kato conjecture can be used to study counterexamples to the classical Lüroth problem. By generalizing a method due to Peyre, we produce for any prime number $\ell $ and any integer $n\geq 2$, a rationally connected, non-rational variety for which non-rationality is detected by a non-trivial degree $n$ unramified étale cohomology class with $\ell $-torsion coefficients. When $\ell = 2$, the varieties that are constructed are furthermore unirational and no
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6

Tamiozzo, Matteo. "On the Bloch–Kato conjecture for Hilbert modular forms." Mathematische Zeitschrift 299, no. 1-2 (2021): 427–58. http://dx.doi.org/10.1007/s00209-020-02689-0.

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AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.
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Voevodsky, Vladimir. "Motives over simplicial schemes." Journal of K-Theory 5, no. 1 (2010): 1–38. http://dx.doi.org/10.1017/is010001030jkt107.

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AbstractThis paper was written as a part of [8] and is intended primarily to provide the definitions and results concerning motives over simplicial schemes, which are used in the proof of the Bloch-Kato conjecture.
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8

Kings, Guido, and Annette Huber. "Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters." Duke Mathematical Journal 119, no. 3 (2003): 393–464. http://dx.doi.org/10.1215/s0012-7094-03-11931-6.

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DUMMIGAN, NEIL. "RATIONAL TORSION ON OPTIMAL CURVES." International Journal of Number Theory 01, no. 04 (2005): 513–31. http://dx.doi.org/10.1142/s1793042105000340.

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Vatsal has proved recently a result which has consequences for the existence of rational points of odd prime order ℓ on optimal elliptic curves over ℚ. When the conductor N is squarefree, ℓ ∤ N and the local root number wp= -1 for at least one prime p | N, we offer a somewhat different proof, starting from an explicit cuspidal divisor on X0(N). We also prove some results linking the vanishing of L(E,1) with the divisibility by ℓ of the modular parametrization degree, fitting well with the Bloch–Kato conjecture for L( Sym2E,2), and with an earlier construction of elements in Shafarevich–Tate gr
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DUMMIGAN, NEIL. "SYMMETRIC SQUARE L-FUNCTIONS AND SHAFAREVICH–TATE GROUPS, II." International Journal of Number Theory 05, no. 07 (2009): 1321–45. http://dx.doi.org/10.1142/s1793042109002699.

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We re-examine some critical values of symmetric square L-functions for cusp forms of level one. We construct some more of the elements of large prime order in Shafarevich–Tate groups, demanded by the Bloch–Kato conjecture. For this, we use the Galois interpretation of Kurokawa-style congruences between vector-valued Siegel modular forms of genus two (cusp forms and Klingen–Eisenstein series), making further use of a construction due to Urban. We must assume that certain 4-dimensional Galois representations are symplectic. Our calculations with Fourier expansions use the Eholzer–Ibukiyama gener
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Dissertations / Theses on the topic "Bloch-Kato conjecture"

1

Harrison, Michael Corin. "On the conjecture of Bloch-Kato for Grossencharacters over Q(i)." Thesis, University of Cambridge, 1992. https://www.repository.cam.ac.uk/handle/1810/251690.

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Tamiozzo, Matteo [Verfasser], and Massimo [Akademischer Betreuer] Bertolini. "On the Bloch-Kato conjecture for Hilbert modular forms / Matteo Tamiozzo ; Betreuer: Massimo Bertolini." Duisburg, 2019. http://d-nb.info/1191690938/34.

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3

Lin, Qiang Flach Matthias. "Bloch-Kato conjecture for the adjoint of H1(X0(N)) with integral Hecke algebra /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-11182003-084742.

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QUADRELLI, CLAUDIO. "Cohomology of Absolute Galois Groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/56993.

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The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group. We define a new class of pro-p groups, called Bloch-K
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Chenevier, Gaëtan. "Familles p-adiques de formes automorphes et applications aux conjectures de Bloch-Kato." Paris 7, 2003. http://www.theses.fr/2003PA077027.

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Mundy, Samuel Raymond. "Eisenstein series for G₂ and the symmetric cube Bloch--Kato conjecture." Thesis, 2021. https://doi.org/10.7916/d8-k3ys-vh32.

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The purpose of this thesis is to construct nontrivial elements in the Bloch--Kato Selmer group of the symmetric cube of the Galois representation attached to a cuspidal holomorphic eigenform 𝐹 of level 1. The existence of such elements is predicted by the Bloch--Kato conjecture. This construction is carried out under certain standard conjectures related to Langlands functoriality. The broad method used to construct these elements is the one pioneered by Skinner and Urban in [SU06a] and [SU06b]. The construction has three steps, corresponding to the three chapters of this thesis. The first ste
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Lin, Qiang. "Bloch-Kato Conjecture for the Adjoint of H¹(X₀(N)) with Integral Hecke Algebra." Thesis, 2004. https://thesis.library.caltech.edu/4595/1/BurnsFlachConjectureForIntegralHeckeAlgebra.pdf.

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<p>Let M be a motive that is defined over a number field and admits an action of a finite dimensional semisimple Q-algebra T. David Burns and Matthias Flach formulated a conjecture, which depends on a choice of Z-order T in T, for the leading coefficient of the Taylor expansion at 0 of the T-equivariant L-function of M. For primes l outside a finite set we prove the l-primary part of this conjecture for the specific case where M is the trace zero part of the adjoint of H¹(X₀(N)) for prime N and where T is the (commutative) integral Hecke algebra for cusp forms of weight 2 and the congruence gr
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Books on the topic "Bloch-Kato conjecture"

1

Coates, John, A. Raghuram, Anupam Saikia, and R. Sujatha, eds. The Bloch–Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015. http://dx.doi.org/10.1017/cbo9781316163757.

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John, Coates, R. Sujatha, A. Raghuram, and Anupam Saikia. Bloch-Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015.

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John, Coates, A. Raghuram, and Anupam Saikia. Bloch Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015.

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John, Coates, R. Sujatha, A. Raghuram, and Anupam Saikia. Bloch-Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015.

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5

Bloch-Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015.

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6

Haesemeyer, Christian, and Charles A. Weibel. The Norm Residue Theorem in Motivic Cohomology. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691191041.001.0001.

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This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It pr
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Book chapters on the topic "Bloch-Kato conjecture"

1

Hulsbergen, Wilfred W. J. "The Bloch-Kato conjecture." In Conjectures in Arithmetic Algebraic Geometry. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-663-09505-7_12.

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Suslin, Andrei, and Vladimir Voevodsky. "Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients." In The Arithmetic and Geometry of Algebraic Cycles. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4098-0_5.

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Conference papers on the topic "Bloch-Kato conjecture"

1

Chebolu, Sunil, and Ján Mináč. "Absolute Galois groups viewed from small quotients and the Bloch–Kato conjecture." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.31.

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