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.

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

Meeting ID: 878 5613 2062