Vector bundles on an elliptic curve over a discrete valuation ring | Posted on:2002-01-06 | Degree:Ph.D | Type:Dissertation | University:The University of Arizona | Candidate:Kim, Seog Young | Full Text:PDF | GTID:1468390014951429 | Subject:Mathematics | Abstract/Summary: | | We classify rank 2 vector bundles on a smooth curve X of genus 1 over a discrete valuation ring R. Atiyah [5] classified rank 2 vector bundles on elliptic curves over algebraically closed fields. The fact that a genus 1 curve over a discrete valuation ring has a codimension 2 subscheme prevents us from applying Atiyah's work directly. We find that genus 1 curve over an arbitrary field can have three types of rank 2 vector bundles.;We classify rank 2 vector bundles on a curve of genus 1 over a discrete valuation ring using the classification on a curve of genus 1 over a field and quadruples ( L,M,Z, eta) where L and M are line bundles on X and Z is a local complete intersection subscheme of codimension 2 and eta is an orbit in Ext1( M⊗IZ,L ) under the R* action. | Keywords/Search Tags: | Vector bundles, Over, Curve, Discrete valuation ring, Genus, Rank | | Related items |
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