07.06.2023 (Wednesday)

Jesse Pajwani (Imperial College London)
07 Jun at 16:00 - 17:00
KCL, Strand - S3.30

The p-adic section conjecture is a long standing conjecture of Grothendieck about curves of high genus over p-adic fields, linking the p-adic points of a curve to sections of a short exact sequence of étale fundamental groups. A powerful way of interpreting the section conjecture is as a fixed point statement, and this interpretation makes the statement look like many other theorems in algebraic topology. For this talk, we'll first introduce the framing of the section conjecture as a fixed point statement, and then show this interpretation allows us to give an alternate proof of part of a result of Pop and Stix towards the section conjecture. This new proof generalises to other fields, and the new fields allow us to extend the original result to a larger class of varieties.

Posted by rachel.newton@kcl.ac.uk