Consider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime $p > 3$. Consider its perfectoid cover $S(p^\infty)$ and the Hodge-Tate period map introduced by A. Caraiani and P. Scholze. We compare the pull-back to $S(p^\infty)$ of the Ekedahl-Oort stratification on the mod p special fiber of S and the pull back to $S(p^\infty)$ of the fine Deligne-Lusztig...
Let k be a field and X a geometrically connected variety over k. The Tate or degeneracy locus of a l-adic local system on X is the etale counterpart of the Hodge locus of a VHS. While in the last decade tremendous progresses have been made in understanding the latter thanks to, in particular, techniques from o-minimality, much less is known about the former. I will review the main conjectures...
The mixing conjecture was proposed by Venkatesh and myself 20 years ago and postulates that pair of CM-points multiplicatively connected equidistribute on products of locally homogeneous space associated to forms of $PGL_2$.
It was established by Khayutin, for sequences of fundamental discriminant splitting two given primes and under the assumption that there is no Landau-siegel zero,using...
