44 citations · 253 across the 45 of their papers we have counts for
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Some cases of the Mumford--Tate conjecture and Shimura varieties
Adrian Vasiu
We prove the Mumford--Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura varieties that are products of simple, adjo…
Manin problems for Shimura varieties of Hodge type
Adrian Vasiu
Let k be a perfect field of characteristic p>0. We prove the existence of ascending and descending slope filtrations for Shimura p-divisible objects over k. We use them to classify…
Surjectivity Criteria for p-adic Representations, Part I
Adrian Vasiu
We prove several surjectivity criteria for -adic representations. In particular, we classify all adjoint and simply connected group schemes over the Witt ring of a fi…
A purity theorem for abelian schemes
Adrian Vasiu
We prove a purity theorem for abelian schemes in arbitrary unramified mixed characteristic (0,p). The case p=2 is completely new and the case p>2 fixes several errors in the litera…
Generalized Serre--Tate Ordinary Theory
Adrian Vasiu
We study a generalization of Serre--Tate theory of ordinary abelian varieties and their deformation spaces. This generalization deals with abelian varieties equipped with additiona…
Crystalline boundedness principle
Adrian Vasiu
We prove that an -crystal $(M,\vph)$ over an algebraically closed field of characteristic is determined by $(M,\vph)$ mod , where depends only on the ran…