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2011•Experimental MathematicsRequires access

Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture

Werner Bley

Open publisher page 16 citations

Abstract

Let be an elliptic curve and a finite Galois extension with group G. We write EK for the base change of E and consider the equivariant Tamagawa number conjecture for the pair (h 1(EK )(1),). This conjecture is an equivariant refinement of the Birch and Swinnerton-Dyer conjecture for E/K. For almost all primes l, we derive an explicit formulation of the conjecture that makes it amenable to numerical verifications. We use this to provide convincing numerical evidence in favor of the conjecture.

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What this paper is about

Let be an elliptic curve and a finite Galois extension with group G. We write EK for the base change of E and consider the equivariant Tamagawa number conjecture for the pair (h 1(EK )(1),). This conjecture is an equivariant refinement of the Birch and Swinnerton-Dyer conjecture for E/K. For almost all primes l, we derive an explicit formulation of the conjecture that makes it amenable to numerical verifications. We use this to provide convincing numerical evidence in favor of the conjecture.

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OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let be an elliptic curve and a finite Galois extension with group G. We write EK for the base change of E and consider the equivariant Tamagawa number conjecture for the pair (h 1(EK )(1),). This conjecture is an equivariant refinement of the Birch and Swinnerton-Dyer conjecture for E/K. For almost all primes l, we derive an explicit formulation of the conjecture that makes it amenable to numerical verifications. We use this to provide convincing numerical evidence in favor of the conjecture.

Key concepts: Conjecture, Equivariant map, Mathematics, Extension (predicate logic), Collatz conjecture, Combinatorics, Pure mathematics, Computer science

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