Local langlands conjecture for gl(2), Bushnell, Colin J. Henniart, Guy

Автор: John Coates; Peter Schneider; R. Sujatha; Otmar Ve
Название: Noncommutative Iwasawa Main Conjectures over Totally Real Fields
ISBN: 3642443354 ISBN-13(EAN): 9783642443350
Издательство: Springer
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Описание: The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

Автор: Coates
Название: The Bloch–Kato Conjecture for the Riemann Zeta Function
ISBN: 1107492963 ISBN-13(EAN): 9781107492967
Издательство: Cambridge Academ
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Описание: An account of a significant body of recent work that resolves some long-standing mysteries concerning special values of the Riemann zeta function. It brings together many important results from K-theory, motivic cohomology, and Iwasawa theory, accessible at graduate level and above.

Автор: Stein Elias, Mather John N., Griffiths Phillip
Название: Weil`s Conjecture for Function Fields: Volume I (Ams-198)
ISBN: 0691182140 ISBN-13(EAN): 9780691182148
Издательство: Wiley
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Описание:

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil's conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil's conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting ℓ-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors.

Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil's conjecture. The proof of the product formula will appear in a sequel volume.

Автор: Gerhard Frey
Название: On Artin`s Conjecture for Odd 2-dimensional Representations
ISBN: 3540583874 ISBN-13(EAN): 9783540583875
Издательство: Springer
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Описание: The objective of this study is to develop efficient algorithms with which to verify Artin's conjecture for odd two-dimensional representations. It is hoped that the algorithms developed for this text can also be used to solve other problems related to modular forms.

Автор: Valerio Capraro; Martino Lupini; Vladimir Pestov
Название: Introduction to Sofic and Hyperlinear Groups and Connes` Embedding Conjecture
ISBN: 3319193325 ISBN-13(EAN): 9783319193328
Издательство: Springer
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Описание: This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices.