Class Field Theory and Arithmetic of Abelian Varieties over Local Fields

Christopher Stephen Hall

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arXiv · 2203.11855

Class Field Theory and Arithmetic of Abelian Varieties over Local Fields

Christopher Stephen Hall

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Abstract

We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working over local fields with a finite residue field to working with local fields with an arbitrary perfect residue field of positive characteristic. We then briefly discuss the Local Class Field Theory implications of such information

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Christopher Stephen Hall. 2022-03-22. Class Field Theory and Arithmetic of Abelian Varieties over Local Fields. https://arxiv.org/abs/2203.11855

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