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arXiv · 0708.0084

Equivariant Birch-Swinnerton-Dyer conjecture for the base change of elliptic curves: An example

Tejaswi Navilarekallu
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Abstract

Let E be an elliptic curved defined over $\Q$ and let $K/\Q$ be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for $h^1(E\times_{\Q} K)(1)$ viewed as a motive over $\Q$ with coefficients in $\Q[G]$ relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper we prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S_3-extension of $\Q$.

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Tejaswi Navilarekallu. 2007-08-01. Equivariant Birch-Swinnerton-Dyer conjecture for the base change of elliptic curves: An example. https://arxiv.org/abs/0708.0084

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