Geodesic
Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case
Documenta mathematica, Tome 27 (2022), pp. 151-182 Cet article a éte moissonné depuis la source EMS Press

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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 dvrR 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.
DOI : 10.4171/dm/868
Classification : 14G35, 14K99, 14L15, 14L30
Mots-clés : abelian varieties, Shimura varieties, essential dimension, finite group schemes 
@article{10_4171_dm_868,
     author = {Rijul Saini and Najmuddin Fakhruddin},
     title = {Finite groups scheme actions and incompressibility of {Galois} covers: beyond the ordinary case},
     journal = {Documenta mathematica},
     pages = {151--182},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/868},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/868/}
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Rijul Saini; Najmuddin Fakhruddin. Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case. Documenta mathematica, Tome 27 (2022), pp. 151-182. doi: 10.4171/dm/868

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