# On Zagier's conjecture for base extensions of elliptic curves

@article{Brunault2012OnZC, title={On Zagier's conjecture for base extensions of elliptic curves}, author={Franccois Brunault}, journal={arXiv: Number Theory}, year={2012} }

Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), where E/F is the base extension of E to F.

## 25 References

### On an elliptic analogue of Zagier’s conjecture

- 1997

Mathematics

§ 1 contains the formulation of the conjecture. The most general context in which it can be stated is that of families of elliptic curves over a base B. However, we give the statement for the image…

### Zagier's conjecture on L(E,2)

- 1995

Mathematics

Abstract. In this paper we introduce an elliptic analog of the Bloch-Suslin complex and prove that it (essentially) computes the weight two parts of the groups K2(E) and K1(E) for an elliptic curve E…

### Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves

- 2011

Mathematics

Introduction Tamagawa numbers Tamagawa numbers. Continued Continuous cohomology A theorem of Borel and its reformulation The regulator map. I The dilogarithm function The regulator map. II The…

### Integral Elements in K-Theory and Products of Modular Curves

- 2000

Mathematics

In the first part of this paper we use de Jong’s method of alterations to contruct unconditionally ‘integral’ subspaces of motivic cohomology (with rational coefficients) for Chow motives over local…

### Be ilinson''s theorem on modular curves

- 1986

Mathematics

0. Introduction. The purpose of this chapter is to give a detailed account of the known evidence ([Be1], §5) for Beilinson’s conjecture concerning the values at s = 2 of L-functions of modular forms…

### Multiplicity one Theorems

- 2007

Mathematics

In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by…

### Classical and Elliptic Polylogarithms and Special Values of L-Series

- 2000

Mathematics

The Dirichlet class number formula expresses the residue at s = 1 of the Dedekind zeta function ζ F(s) of an arbitrary algebraic number field F as the product of a simple factor (involving the class…

### The Arithmetic and Geometry of Algebraic Cycles

- 2000

Mathematics

Preface. Conference Programme. Conference Picture. List of participants. Authors' addresses. Cohomological Methods. Lectures on algebro-geometric Chern-Weil and Cheeger-Chern-Simons theory for vector…

### The Equivariant Tamagawa Number Conjecture: A survey

- 2003

Mathematics

We give a survey of the equivariant Tamagawa number (a.k.a. Bloch-Kato) conjecture with particular emphasis on proven cases. The only new result is a proof of the 2-primary part of this conjecture…

### Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields

- 1991

Mathematics

The Dedekind zeta function ζF(s) of an algebraic number field F is the most important invariant of F. Its Euler product tells how the unramified primes of Q split in F. Information about the ramified…