Some fundamental groups in arithmetic geometry

2015/12/30 by Hélène Esnault, Esnault, Hélène
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1512.08876

openalex publication_date 2015/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Those are the notes for the 2015 Summer Research Institute on Algebraic Geometry. We report on Deligne's finiteness theorem for ℓ-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.

Related

• Arithmetic representations of fundamental groups II: finiteness
• Finiteness of étale fundamental groups by reduction modulo p
• Fundamental groups of proper varieties are finitely presented
• Semisimplicity and weight-monodromy for fundamental groups
• Fundamental groups and good reduction criteria for curves over positive\n characteristic local fields