Show simple item record

dc.contributor.authorMaulik, Davesh
dc.date.accessioned2018-05-29T13:33:21Z
dc.date.available2018-05-29T13:33:21Z
dc.date.issued2014-10
dc.identifier.issn0012-7094
dc.identifier.issn1547-7398
dc.identifier.urihttp://hdl.handle.net/1721.1/115923
dc.description.abstractGiven a K3 surface X over a field of characteristic p, Artin conjectured that if X is supersingular (meaning infinite height), then its Picard rank is 22. Along with work of Nygaard–Ogus, this conjecture implies the Tate conjecture for K3 surfaces over finite fields with p≥5. We prove Artin’s conjecture under the additional assumption that X has a polarization of degree 2d with p>2d+4. Assuming semistable reduction for surfaces in characteristic p, we can improve the main result to K3 surfaces which admit a polarization of degree prime to p when p≥5. The argument uses Borcherds’s construction of automorphic forms on O(2,n) to construct ample divisors on the moduli space. We also establish finite-characteristic versions of the positivity of the Hodge bundle and the Kulikov–Pinkham–Persson classification of K3 degenerations. In the appendix by A. Snowden, a compatibility statement is proven between Clifford constructions and integral p-adic comparison functors.en_US
dc.publisherDuke University Pressen_US
dc.relation.isversionofhttp://dx.doi.org/10.1215/00127094-2804783en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleSupersingular K3 surfaces for large primesen_US
dc.typeArticleen_US
dc.identifier.citationMaulik, Davesh. “Supersingular K3 Surfaces for Large Primes.” Duke Mathematical Journal, 163, 13 (October 2014): 2357–2425en_US
dc.contributor.mitauthorMaulik, Davesh
dc.relation.journalDuke Mathematical Journalen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2018-05-24T18:31:12Z
dspace.orderedauthorsMaulik, Daveshen_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-7525-318X
mit.licenseOPEN_ACCESS_POLICYen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record