Abelian surfaces with supersingular good reduction and non semisimple Tate module

Maja Volkov

Abelian surfaces with supersingular good reduction and non semisimple Tate module

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arxiv 2301.05564 v1 pith:CQL5RS4X submitted 2023-01-13 math.NT

Maja Volkov This is my paper · ORCID

classification math.NT

keywords abeliangoodmodulereductionsemisimplesupersingularsurfacesadic

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abstract

We show the existence of abelian surfaces $A$ over $\mathbb{Q}_p$ having good reduction with supersingular special fibre whose associated $p$-adic Galois module $V_p(A)$ is not semisimple.

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Monodromy Groups of Supersingular Abelian Surfaces over $\mathbb{Q}_p$
math.NT 2025-11 accept novelty 7.0 of 10

For p≥7, the neutral components of p-adic monodromy groups of supersingular abelian surfaces over Q_p are classified and shown to be generically isomorphic to GL_2 ×_det GL_2.

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