Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case
Najmuddin FakhruddinSchool of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Rijul SainiSchool of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Inspired by recent work of B. Farb et al. [Compos. Math. 157, No. 11, 2407--2432 (2021; Zbl 1490.14042)], we develop a method for using actions of finite group schemes over a mixed characteristic to get lower bounds for the essential dimension of a cover of a variety over . We then apply this to prove -incompressibility for congruence covers of a class of unitary Shimura varieties for primes at which the reduction of the Shimura variety (at any prime of the reflex field over does not have any ordinary points. We also make some progress towards a conjecture of Brosnan on the -incompressibility of the multiplication by map of an abelian variety.
Cite this article
Najmuddin Fakhruddin, Rijul Saini, Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case. Doc. Math. 27 (2022), pp. 151–182DOI 10.4171/DM/868