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On the integral 2-adic Tate module of elliptic curves

Edwina Aylward

math.NTarXiv:2608.17725

Abstract

We show that the integral 2-adic Tate module of an elliptic curve over a complete discretely valued field of odd residue characteristic is determined by its 2-torsion representation, together with the square class of c and local information about the pairwise differences of the roots of f in a model E y2=cf(x), where f is monic of degree 3. The proof uses explicit halving formulae to determine the Galois action on the full tower of 2-power torsion.

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