# 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 - המחלקה למתמטיקה 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.

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

Meeting ID: 878 5613 2062

תאריך עדכון אחרון : 13/10/2021