5 papers
McKay correspondence for linearly reductive finite group schemes in positive characteristic
Matthew Satriano, Jeremy Usatine
We obtain a motivic and a cohomological McKay correspondence for finite linearly reductive group schemes in arbitrary characteristic. In particular, we prove that if is a finit…
A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers
Matthew Satriano, Jeremy Usatine
Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integ…
Beyond twisted arcs: a McKay correspondence for reductive groups
Matthew Satriano, Jeremy Usatine
We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne--Mumford stacks, warped maps are…
A cohomological interpretation for stringy Hodge numbers
Jiahui Huang, Matthew Satriano, Jeremy Usatine
We obtain a cohomological interpretation for Batyrev's stringy Hodge numbers in the full generality in which they are defined. In a previous paper, the second and third authors use…
Stringy Hodge numbers via crepant resolutions by Artin stacks
Matthew Satriano, Jeremy Usatine
In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby pro…