Journal ArticleDOI
Equivariant Epsilon Constants, Discriminants and Étale Cohomology
Werner Bley,David Burns +1 more
TLDR
In this paper, the authors formulate and study a conjectural equality between an element of the relative algebraic K-group $K_0(\mathbb{Z}[\mathrm{Gal}(L/K)], \mathbb {R})$ which is constructed from the equivariant Artin epsilon constant of the L/K constant and a sum of structural invariants associated to the L-function.Abstract:
Let $L/K$ be a finite Galois extension of number fields. We formulate and study a conjectural equality between an element of the relative algebraic K-group $K_0(\mathbb{Z}[\mathrm{Gal}(L/K)], \mathbb{R})$ which is constructed from the equivariant Artin epsilon constant of $L/K$ and a sum of structural invariants associated to $L/K$. The precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the Tamagawa Number Conjecture of Bloch and Kato (as formulated by Flach and the second-named author) should be compatible with the functional equation of the associated L-function. We show that, more concretely, our conjecture also suggests a completely systematic refinement of the central approach and results of classical Galois module theory. In particular, the evidence for our conjecture that we present here already strongly refines many of the main results of Galois module theory.read more
Citations
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Journal ArticleDOI
On the Equivariant Tamagawa number conjecture for Tate motives
David Burns,C Greither +1 more
TL;DR: 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)]).
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.
Journal Article
Equivariant Weierstrass Preparation and Values of L-functions at Negative Integers
TL;DR: In this article, an equivariant version of the p-adic Weierstrass Preparation Theorem is applied in the context of possible non-commutative gen- eralizations of the power series of Deligne and Ribet.
Journal ArticleDOI
On derivatives of Artin L-series
TL;DR: In this article, a universal theory of refined Stark conjectures is presented, including a full proof in several important cases, and explain the connection to previous conjectures of Bloch and Kato, of Lichtenbaum and of Serre and Tate.
Journal ArticleDOI
On the equivariant Tamagawa number conjecture in tame CM-extensions
Andreas Nickel,Andreas Nickel +1 more
TL;DR: In this paper, the Equivariant Tamagawa Number Conjecture (ETNC) was shown to imply Strong Brumer-Stark Conjectures at p for almost all primes p.
References
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The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
Finn F. Knudsen,David Mumford +1 more
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Tamagawa numbers for motives with (non-commutative) coefficients.
David Burns,Matthias Flach +1 more
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LES CONJECTURES DE STARK SUR LES FONCTIONS L d'ARTIN EN s = 0 (Progress in Mathematics, 47)
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Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I
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On Fröhlich's conjecture for rings of integers of tame extensions
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