Nearby cycles and semipositivity in positive characteristic
Algebraic Geometry
2023-01-31 v3
Abstract
We study restriction of logarithmic Higgs bundles to the boundary divisor and we construct the corresponding nearby-cycles functor in positive characteristic. As applications we prove some strong semipositivity theorems for analogs of complex polarized variations of Hodge structures and their generalizations. This implies, e.g., semipositivity for the relative canonical divisor of a semistable reduction in positive characteristic and it gives some new strong results generalizing semipositivity even for complex varieties.
Keywords
Cite
@article{arxiv.1902.05745,
title = {Nearby cycles and semipositivity in positive characteristic},
author = {Adrian Langer},
journal= {arXiv preprint arXiv:1902.05745},
year = {2023}
}
Comments
v2: corrected grant number v3: various corrections and improvements; 54 pages