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arXiv · 1912.12797

Local Oort groups and the isolated differential data criterion

Huy Dang·Soumyadip Das·Kostas Karagiannis·Andrew Obus·Vaidehee Thatte
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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.

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Huy Dang, Soumyadip Das, Kostas Karagiannis, Andrew Obus, Vaidehee Thatte. 2019-12-30. Local Oort groups and the isolated differential data criterion. https://doi.org/10.5802/jtnb.1200

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