Nearby cycles and semipositivity in positive characteristic

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.

v2: corrected grant number v3: various corrections and improvements; 54 pages

References in corpus (3)

• Logarithmic nonabelian Hodge theory in characteristic p
• Semi-positivity from Higgs bundles
• Projective Crystalline Representations of Étale Fundamental Groups and Twisted Periodic Higgs-de Rham Flow

Cited by in corpus (4)

• Positivity vs. slope semistability for bundles with vanishing discriminant
• Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
• Periodic de Rham bundles over curves
• A Lefschetz theorem for crystalline representations