Vector bundles on an elliptic curve over a discrete valuation ring
Author
Kim, Seog YoungIssue Date
2001Keywords
Mathematics.Advisor
Kim, Minhyong
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
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, η) where L and M are line bundles on X and Z is a local complete intersection subscheme of codimension 2 and η is an orbit in Ext¹(M⊗I(z),L ) under the R* action.Type
textDissertation-Reproduction (electronic)
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics