Models of curves : the birch and Swinnerton-Dyer conjecture & ordinary reduction

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Models of curves : the birch and Swinnerton-Dyer conjecture & ordinary reduction

Type: Doctoral Thesis
Title: Models of curves : the birch and Swinnerton-Dyer conjecture & ordinary reduction
Author: Bommel, R. van
Issue Date: 2018-10-31
Keywords: Birch-Swinnerton-Dyer conjecture
Jacobians
Curves
Covers
Deformation theory
P-rank
Isogeny
Abstract: Chapter 1,contains the numerical verification of the Birch and Swinnerton-Dyer conjecture for hundreds of Jacobians of hyperelliptic curves of genus 2, 3, 4 and 5. Chapter 2 treats the equivalence of BSD for a certain elliptic curve over Q(∜5), and a pair of hyperelliptic curves over Q. In chapter 3, ordinary Galois covers of smooth curves are constructed from ordinary Galois covers of semi-stable curves. Finally, in chapter 4, the statistics of ordinary reduction for hyperelliptic curves is considered.
Promotor: Supervisor: Edixhoven S.J. Co-Supervisor: Holmes D.S.T., Pazuki F.M.
Faculty: Faculty of Science
University: Leiden University
Handle: http://hdl.handle.net/1887/66673
 

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application/pdf Chapter 1 473.3Kb View/Open
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application/pdf Bibliography 237.0Kb View/Open
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