Some fundamental groups in arithmetic geometry

Hélène Esnault

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arXiv · 1512.08876

Some fundamental groups in arithmetic geometry

Hélène Esnault

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Abstract

Those are the notes for the 2015 Summer Research Institute on Algebraic Geometry. We report on Deligne's finiteness theorem for $\ell$-adic representations on smooth varieties defined over a finite field, on its crystalline version, and on how the geometric étale fundamental group of a smooth projective variety defined over a characteristic $p>0$ field controls crystals on the infinitesimal site and should control those on the crystalline site. v2: last results added to the report, and some typos corrected.

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Hélène Esnault. 2016-09-08. Some fundamental groups in arithmetic geometry. https://arxiv.org/abs/1512.08876

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