Local Galois Symbols on E x E

2008/08/07 by Jacob P. Murre, Dinakar Ramakrishnan, Murre, Jacob +1
Computer Science · Mathematics · #11G07 #11G25 #11S25 #14C15 #14C25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0808.1129

openalex publication_date 2008/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is the first part of a two-part work on the Albanese kernel T_F(E x E), for an elliptic curve E over F. The main result furnishes information, for any odd prime p, about the kernel and image of the Galois symbol map from T_F(E × E)/p to the Galois cohomology group H²(F, E[p] (x) E[p]), for F a p-adic field and E/F ordinary, without requiring that the p-torsion points are F-rational. A key step is to show that the image is zero when the Galois module E[p] is non-semisimple. The forthcoming second part will deal with global questions.

Citations

• Algebraic Groups Over Finite Fields

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