The tame fundamental group schemes of curves in positive characteristic

2018/02/04 by Otabe, Shusuke
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.01111

Abstract

The tame fundamental group scheme for an algebraic variety is the maximal linearly reductive quotient of Nori's fundamental group scheme. In this paper, we study the tame fundamental group schemes of smooth curves defined over algebraically closed fields of positive characteristic and develop the theory of cospecialization maps for them. As a result, we see that the tame fundamental group schemes heavily depend on the curves. We also see that numerical invariants of curves can be reconstructed from the tame fundamental group schemes.

Related

• Finite presentation of the tame fundamental group
• Fundamental group schemes of globally F-regular varieties
• The tame Nori fundamental group
• Anabelian properties of tame fundamental groups of singular curves
• Tame stacks in positive characteristic