Galois cohomology of function fields of curves over non-archimedean local fields
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- by Saurabh Gosavi PDF
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Abstract:
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 of the local field. In this article, we show that every element in $H^{3}(F, \mu _{m}^{\otimes 2})$ is of the form $\chi \cup (f) \cup (g)$, where $\chi$ is in $H^{1}(F, \mathbb {Z}/m\mathbb {Z})$ and $(f)$, $(g)$ in $H^{1}(F, \mu _{m})$. This extends a result of Parimala and Suresh [Ann. of Math. (2) 172 (2010), pp. 1391–1405], where they show this when $m$ is prime and when $F$ contains $\mu _{m}$.References
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Additional Information
- Saurabh Gosavi
- Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel, 5290002.
- MR Author ID: 1229871
- Email: gosavis@biu.ac.il
- Received by editor(s): May 20, 2021
- Received by editor(s) in revised form: February 14, 2022, and March 2, 2022
- Published electronically: August 12, 2022
- Additional Notes: This research was partially supported by the Israel Science Foundation (grant no. 630/17).
- Communicated by: Romyar T. Sharifi
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5179-5191
- MSC (2020): Primary 12G05
- DOI: https://doi.org/10.1090/proc/16074