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arXiv · 2103.04197

Vari\'et\'es ab\'eliennes CM et grosse monodromie finie sauvage

Séverin Philip
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Abstract

In this paper we study the wild part of the finite monodromy groups of abelian varieties over number fields. We solve Grunwald problems for groups of the form $\mathbf{Z}/p\mathbf{Z}\wr \mathfrak{S}_n$ over number fields to build CM abelian varieties with maximal wild finite monodromy in the odd prime case. For the even prime case we prove a new bound on the 2-part of the order of the finite monodromy group for CM abelian varieties and build varieties that reach it.

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Séverin Philip. 2021-03-06. Vari\'et\'es ab\'eliennes CM et grosse monodromie finie sauvage. https://arxiv.org/abs/2103.04197

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