Local Oort groups and the isolated differential data criterion
Algebraic Geometry
2024-12-17 v2 Commutative Algebra
Abstract
It is conjectured that if k is an algebraically closed field of characteristic p > 0, then any branched G-cover of smooth projective k-curves where the "KGB" obstruction vanishes and where a p-Sylow subgroup of G is cyclic lifts to characteristic 0. Obus has shown that this conjecture holds given the existence of certain meromorphic differential forms on P_1^k with behavior determined by the ramification data of the cover. We give a more efficient computational procedure to compute these forms than was previously known. As a consequence, we show that all D_25- and D_27-covers lift to characteristic zero.
Cite
@article{arxiv.1912.12797,
title = {Local Oort groups and the isolated differential data criterion},
author = {Huy Dang and Soumyadip Das and Kostas Karagiannis and Andrew Obus and Vaidehee Thatte},
journal= {arXiv preprint arXiv:1912.12797},
year = {2024}
}
Comments
Minor edits, still 16 pages