๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the equivariant Tamagawa number conjecture for -extensions of number fields

โœ Scribed by Tejaswi Navilarekallu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
243 KB
Volume
121
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

For a finite Galois extension K/k of number fields, with Galois group G, the equivariant Tamagawa number conjecture of Burns and Flach relates the leading coefficients of Artin L-functions to an element of K 0 (Z[G], R) arising from the Tate sequence. This conjecture is known to be true for certain non-abelian Galois extensions over Q with Galois group being the dihedral or quaternion group. In this article, we shall verify the conjecture for an A 4 -extension over Q, by explicitly constructing the Tate sequence using Chinburg's methods.

๐Ÿ“œ SIMILAR VOLUMES

On the tamagawa number conjecture for he
On the tamagawa number conjecture for hecke characters
โœ Francesc Bars ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 268 KB

## Abstract In this paper, we prove the weak __p__โ€part of the Tamagawa number conjecture in all nonโ€critical cases for the motives associated to Hecke characters of the form $\varphi ^a\overline{\varphi }^b$ where ฯ† is the Hecke character of a CM elliptic curve __E__ defined over an imaginary quad

On the Tamagawa Number Conjecture for CM
On the Tamagawa Number Conjecture for CM Elliptic Curves Defined Over Q
โœ Francesc Bars ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 206 KB

In this paper we prove, under the assumption that the Souleยดregulator map is injective, that, for all integers k50, the description by the local Tamagawa number conjecture for CM elliptic curves defined over Q, corresponding to the values of their L-functions at k รพ 2, is true.

Finiteness Conjectures for Fl[[T]]-Analy
Finiteness Conjectures for Fl[[T]]-Analytic Extensions of Number Fields
โœ Gebhard Bรถckle ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 193 KB

We formulate a finiteness conjecture on the image of the absolute Galois group of totally real fields under an even linear representation over a local field of positive characteristic. This is motivated by a recent conjecture of de Jong in the function field case. We discuss the relation to some con

On the Fontaineโ€“Mazur Conjecture for Num
On the Fontaineโ€“Mazur Conjecture for Number Fields and an Analogue for Function Fields
โœ Joshua Brandon Holden ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 339 KB

The Fontaine Mazur Conjecture for number fields predicts that infinite l-adic analytic groups cannot occur as the Galois groups of unramified l-extensions of number fields. We investigate the analogous question for function fields of one variable over finite fields, and then prove some special cases