Abstract

Let C be a hyperelliptic curve of good reduction defined over a discrete valuation field K. Given d ∈ K∗ \K∗2, we find the minimal regular model of the quadratic twist of C by d. Then we prove that there exists an infinite family of hyperelliptic curves of genus 2 defined over Q violating the Hasse principle.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.