Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions
نویسندگان
چکیده
et E be an elliptic curve defined 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 describe a reinterpretation of the Equivariant Tamagawa Number Conjecture (‘ETNC’) for E, 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 E, 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. This is a report on joint work with Daniel Macias Castillo Host: James McKernan Wednesday, November 8, 2017 2:30 PM AP&M 2402 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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