Universiteit Leiden

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Dissertation

Models of curves: The Birch and Swinnerton-Dyer conjecture & ordinary reduction

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.

Author
Bommel, R. van
Date
31 October 2018
Links
Thesis in Leiden Repository

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.

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