Genus 1 curves in twisted projective spaces

Abstract: Does every Severi—Brauer variety contain a (possibly singular) genus 1 curve? This basic question was asked by David Saltman and Pete Clark and answered in low dimensions by Johan de Jong and Wei Ho. I will explain something of the history of the problem as well as recent joint work with Asher Auel where we show, with the help of a nice observation of David Saltman, that the answer is `yes’ for twisted forms of $\mathbb{P}^r$ for $r=6$ over global fields.

algebraic geometry

Audience: researchers in the topic

Comments: The discussion for Ben Antieau’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-01-15-ba (and will be deleted after ~3-7 days).

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com