Local Oort groups and the isolated differential data criterion
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866929629180198912 |
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| author | Dang, Huy Das, Soumyadip Karagiannis, Kostas Obus, Andrew Thatte, Vaidehee |
| author_facet | Dang, Huy Das, Soumyadip Karagiannis, Kostas Obus, Andrew Thatte, Vaidehee |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_12797 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Local Oort groups and the isolated differential data criterion Dang, Huy Das, Soumyadip Karagiannis, Kostas Obus, Andrew Thatte, Vaidehee Algebraic Geometry Commutative Algebra 14H37, 12F10, 13B05 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. |
| title | Local Oort groups and the isolated differential data criterion |
| topic | Algebraic Geometry Commutative Algebra 14H37, 12F10, 13B05 |
| url | https://arxiv.org/abs/1912.12797 |