B. Poonen

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math.AG2025

The valuation of the discriminant of a hypersurface

Bjorn Poonen, Michael Stoll

Let $R$ be a discrete valuation ring, with valuation $v : R ↠ Z_{\geq 0} \cup {\infty}$ and residue field $k$ . Let $H$ be a hypersurface $\operatorn…

math.AG2025

Lattices in Tate modules

Bjorn Poonen, Sergey Rybakov

Refining a theorem of Zarhin, we prove that given a $g$ -dimensional abelian variety $X$ and an endomorphism $u$ of $X$ , there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z…