Mordell-Weil group as Galois modules

2023/06/23 by Vavasour, Thomas, Wuthrich, Christian
#11G05 #11G07 #20C10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.13365

Abstract

We study the action of the Galois group G of a finite extension K/k of number fields on the points on an elliptic curve E. For an odd prime p, we aim to determine the structure of the p-adic completion of the Mordell-Weil group E(K) as a ℤ_p[G]-module only using information of E over k and the completions of K.

Related

• Realizing Rational Representations in Mordell-Weil Groups
• Elliptic curves and finitely generated Galois groups
• Steinitz class of Mordell groups of elliptic curves with complex multiplication
• Heegner points and Mordell-Weil groups of elliptic curves over large fields
• Mordell-Weil groups and the rank of elliptic curves over large fields