Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case

2021/02/11 by Fakhruddin, Najmuddin, Saini, Rijul · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.05993

Abstract

Inspired by recent work of Farb, Kisin and Wolfson, we develop a method for using actions of finite group schemes over a mixed characteristic dvr R to get lower bounds for the essential dimension of a cover of a variety over K = Frac(R). We then apply this to prove p-incompressibility for congruence covers of a class of unitary Shimura varieties for primes p at which the reduction of the Shimura variety (at any prime of the reflex field over p) does not have any ordinary points. We also make some progress towards a conjecture of Brosnan on the p-incompressibility of the multiplication by p map of an abelian variety.

Cited by

• Essential dimensions of polarized endomorphisms of abelian varieties

Related

• Fixed points, local monodromy, and incompressibility of congruence covers
• Field of moduli and field of definition of Galois covers
• Essential dimension relative to branched covers of degree at most n
• The fields of definition of branched Galois covers of the projective line
• Group actions on Jacobian varieties