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Bley, Werner and Macias Castillo, Daniel (2017): Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions. In: Journal für Die Reine und Angewandte Mathematik, Vol. 722: pp. 105-135

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Let A be an abelian variety over a number field k and let F be 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 congruences 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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