46 citations · 236 across the 29 of their papers we have counts for
33 papers
Potential isotriviality of isocrystals and proper covers
Adrian Langer, Lei Zhang
We study convergent and overconvergent isocrystals that become trivial after pullback along a proper surjective morphism. On a geometrically unibranch variety over an algebraically…
Weak positivity and weak flatness of vector bundles
Adrian Langer
We study Viehweg's weak positivity for vector bundles on quasi-projective schemes over noetherian rings, including mixed characteristic. We prove that weak positivity is preserved…
Ample vector bundles on non-proper schemes
Adrian Langer
We solve two open problems on ample vector bundles posed by Hartshorne in 1966. We prove that tensor products of ample vector bundles on schemes of finite type over an algebraicall…
Isocrystals on unibranch varieties and open immersions
Adrian Langer, Lei Zhang
We prove that for a connected, geometrically unibranch variety over a perfect field of positive characteristic and a dense open subset , the canonical homomorphism…
Simpson's correspondence on singular varieties in positive characteristic
Adrian Langer
The main aim of the paper is to provide analogues of Simpson's correspondence on singular projective varieties defined over an algebraically closed field of characteristic . T…
Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
Adrian Langer
We prove Bogomolov's inequality on a normal projective variety in positive characteristic and we use it to show some new restriction theorems and a new boundedness result. Then we…