Geodesic
Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case
Documenta mathematica, Tome 27 (2022), pp. 151-182.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Inspired by recent work of \textit{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 $\mathrm{dvr}\,\,\mathbb{R}$ to get lower bounds for the essential dimension of a cover of a variety over $K = \text{Frac}(\mathbb{R})$. 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.
Classification : 14L30, 14G35, 14K99
Keywords: essential dimension, finite group schemes, Shimura varieties, abelian varieties 
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     title = {Finite groups scheme actions and incompressibility of {Galois} covers: beyond the ordinary case},
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Fakhruddin, Najmuddin; Saini, Rijul. Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case. Documenta mathematica, Tome 27 (2022), pp. 151-182. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a63/