Journal ArticleDOI
On the Equivariant Tamagawa number conjecture for Tate motives
David Burns,C Greither +1 more
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TLDR
In this paper, the Equivariant Tamagawa Number Conjecture for finite abelian extensions of ℚ was proved for any integer r with r ≥ 0. And for each integer r > 0, it was shown that the pair (h 0(Spec(L))(r),ℤ[½][Gal(L/K)]).Abstract:
Let L be a finite abelian extension of ℚ and let K be any subfield of L. For each integer r with r≤0 we prove the Equivariant Tamagawa Number Conjecture for the pair (h
0(Spec(L))(r),ℤ[½][Gal(L/K)]).read more
Citations
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Journal ArticleDOI
Arithmetic duality theorems
TL;DR: The complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry can be found in this paper, where the authors provide a good introduction to the subject.
Journal Article
Tamagawa numbers for motives with (non-commutative) coefficients.
David Burns,Matthias Flach +1 more
TL;DR: In this paper, Taylor et al. formulate and study a conjecture for the leading coefficient of the Taylor expansion at 0 of the A-equivariant L-function of a semisimple Q-algebra.
Journal ArticleDOI
The tamagawa number conjecture of adjoint motives of modular forms
TL;DR: In this paper, Taylor and Wiles showed that the mod λ representation associated to a new form of weight k ⩾ 2, level N with coefficients in a number field K, and A the adjoint motive of the motive M associated to f, is irreducible when restricted to the Galois group over Q ( − 1 ) ( l − 1 / 2 l ) where λ | l.
The Equivariant Tamagawa Number Conjecture: A survey
Matthias Flach,C. Greither +1 more
TL;DR: In this paper, a survey of the equivariant Tamagawa number conjecture with particular emphasis on proven cases is given, where the only new result is a proof of the 2-primary part of this conjecture for Tate-motives over abelian fields.
Journal ArticleDOI
Tamagawa numbers for motives with (noncommutative) coefficients, II
David Burns,Matthias Flach +1 more
TL;DR: In this article, the authors provide corroborative evidence for the equivariant Tamagawa number conjecture, which was first formulated in the first part of this article, and then proved in the second part.
References
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Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
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Introduction to Cyclotomic Fields
TL;DR: In this paper, Dirichlet characters were used to construct p-adic L-functions and Bernoulli numbers, which are then used to define the class number formula.
Journal ArticleDOI
Arithmetic duality theorems
TL;DR: The complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry can be found in this paper, where the authors provide a good introduction to the subject.
Book ChapterDOI
Stable real cohomology of arithmetic groups
TL;DR: In this article, it was shown that if a certain quadratic form depending on q is positive non-degenerate, then any Γ-invariant harmonic q-form is automatically G-Invariant.
Book
Arithmetic Duality Theorems
TL;DR: The complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry can be found in this paper, where the authors provide a good introduction to the subject.
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