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arXiv · 1305.1024

Construction of Abelian varieties with given monodromy

Oliver Bueltel
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Abstract

Let $\rho$ be a finite-dimensional faithful representation of a semisimple algebraic group $G$. By means of a deformation argument, we show that there exists a family of Abelian varieties over a smooth and projective curve over the algebraic closure of a prime field of positive characteristic, such that its $\ell$-adic monodromy group covers $G$ and its $\ell$-adic monodromy representation contains $\rho$.

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Oliver Bueltel. 2013-05-05. Construction of Abelian varieties with given monodromy. https://arxiv.org/abs/1305.1024

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