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arXiv · 1405.5001

Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions

Werner Bley·Daniel Macias Castillo
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Abstract

Let A be an abelian variety over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we obtain a reinterpretation of the equivariant Tamagawa number conjecture (eTNC) for A, F/k and p as an explicit family of p-adic congru- ences involving values of derivatives of the Hasse-Weil L-functions of twists of A, normalised by completely explicit twisted regulators. This reinterpretation makes the eTNC amenable to numerical verification and furthermore leads to explicit predictions which refine well-known conjectures of Mazur and Tate.

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Werner Bley, Daniel Macias Castillo. 2014-05-20. Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions. https://arxiv.org/abs/1405.5001

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