# Higher dimensional analogue of cyclicity over $p$-adic curves

Seminar

Speaker

Dr. Saurabh Gosavi (Bar-Ilan University)

Date

20/10/2021 - 11:30 - 10:30Add to Calendar

`2021-10-20 10:30:00``2021-10-20 11:30:00``Higher dimensional analogue of cyclicity over $p$-adic curves``Recall that every division algebra over a number field is cyclic. In this talk, we will show a higher dimensional analogue of this classical fact. More precisely, let $F$ be the function field of a curve over a non-archimedean local field. Let $m \geq 2$ be an integer coprime to the characteristic of the residue field. We will show that every element in $H^{3}(F, \mu_{m}^{\otimes 2})$ is a symbol. This extends a result of Parimala and Suresh where they show this when $m$ is prime and under the assumption that $F$ contains a primitive $m^{th}$ root of unity. ==================================================== https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062``Third floor seminar room, Mathematics building, and on Zoom. See link below.``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room, Mathematics building, and on Zoom. See link below.

Abstract

Recall that every division algebra over a number field is cyclic. In this talk, we will show a higher dimensional analogue of this classical fact. More precisely, let $F$ be the function field of a curve over a non-archimedean local field. Let $m \geq 2$ be an integer coprime to the characteristic of the residue field. We will show that every element in $H^{3}(F, \mu_{m}^{\otimes 2})$ is a symbol. This extends a result of Parimala and Suresh where they show this when $m$ is prime and under the assumption that $F$ contains a primitive $m^{th}$ root of unity.

====================================================

https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 13/10/2021