University of Cambridge > Talks.cam > Number Theory Seminar > Explicit Chabauty over Number Fields

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹī¸ Information

Explicit Chabauty over Number Fields

Download to your calendar using vCal

If you have a question about this talk, please contact Tom Fisher .

Let C be a curve of genus at least 2 over a number field K of degree d. Let J be the Jacobian of C and r the rank of the Mordell-Weil group J(K). Chabauty is a practical method for explicitly computing C(K) provided r <= g – 1. In unpublished work, Wetherell suggested that Chabauty’s method should still be applicable provided the weaker bound r <= d (g – 1) is satisfied. We give details of this and use it to solve the Diophantine equation x2 + y3 = z10 by reducing the problem to determining the K-rational points on several genus 2 curves over K = Q(cube root of 2).

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

Note that ex-directory lists are not shown.

Other lists

Rheumatology Seminar Room, Dept of Medicine, Level 5, Ramsden Room, St. Catharine's College, Trumpington Street, Cambridge, CB2 1RL CISA

Other talks

Title to be confirmed Market Failure, Organ Shortage, Pandemic and Climate Change: The Architecture of Cooperation Online Causal Inference Seminar Welcome Reception and Poster Session Talk title TBC Title to be confirmed
 

Š 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity