Quadratic Chabauty for Atkin-Lehner quotients of modular curves and Shimura curves
Organizer: Timo Keller
Supported by a WiN-UBT 2021 Conference Grant
Date and place
–
at Universität Bayreuth, Bayreuth, Germany
Participants
- Nikola Adžaga (University of Zagreb)
- Lea Beneish (UC Berkeley, remote)
- Shiva Chidambaram (MIT, remote)
- Stevan Gajović (Max-Planck-Institut Bonn, remote)
- Pip Goodman (Max-Planck-Institut Bonn)
- Timo Keller (Leibniz Universität Hannover)
- Angelos Koutsianas (Aristotle University of Thessaloniki)
- Oana Padurariu (Boston University, remote)
- Ciaran Schembri (Dartmouth College)
- Himanshu Shukla (Universität Bayreuth)
- John Voight (Dartmouth College, remote)
- Borna Vukorepa (University of Zagreb, remote)
- Boya Wen (University of Wisconsin-Madison, remote)
Aim of the conference
We work on extending our computation Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6 of the rational points on the modular curves X0+(p) of genus 4, 5, and 6, and the one on hyperelliptic Atkin-Lehner quotients from Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings, to cover more general
- Atkin-Lehner quotients, and
- Shimura curves.
To this end, we extend the quadratic Chabauty algorithm to
- compute local heights away from p, and
- determine the quadratic Chabauty function when there are not many rational points,
for examples of Atkin-Lehner quotients of X0(N) with N square-free.