On the Galois structure of Selmer groups

2015/05/18 by David Burns, Daniel Macias Castillo, Burns, David +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1505.04642

openalex publication_date 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the explicit Galois structure of the p-primary Selmer group of A over F. We also use the results so obtained to derive new bounds on the growth of the Selmer rank of A over extensions of k.

Citations

• Finding large Selmer rank via an arithmetic theory of local constants

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