Skip to Main content Skip to Navigation
Theses

Isogeny graphs, modular polynomials, and applications

Abstract : My thesis looks at ordinary abelian varieties defined with maximal real multiplication. I define modular polynomials in this setting and give an algorithm to compute them over the complex numbers, and for surfaces over finite fields. I also give a structure theorem for isogeny graphs in this setting. I give a generalisation of Schoof-Elkies-Atkin to genus 2 curves with fixed maximal real multiplication using the modular polynomials.
Document type :
Theses
Complete list of metadata

Cited literature [78 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01992715
Contributor : Abes Star :  Contact
Submitted on : Thursday, January 24, 2019 - 3:34:22 PM
Last modification on : Saturday, December 4, 2021 - 3:43:38 AM
Long-term archiving on: : Thursday, April 25, 2019 - 2:39:35 PM

File

MARTINDALE_CHLOE_2018.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01992715, version 1

Collections

Citation

Chloe Martindale. Isogeny graphs, modular polynomials, and applications. Number Theory [math.NT]. Université de Bordeaux; Universiteit Leiden (Leyde, Pays-Bas), 2018. English. ⟨NNT : 2018BORD0086⟩. ⟨tel-01992715⟩

Share

Metrics

Les métriques sont temporairement indisponibles