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Hermitian $ u$-invariants over function fields of $ p$-adic curves


Author: Zhengyao Wu
Journal: Proc. Amer. Math. Soc. 146 (2018), 909-920
MSC (2010): Primary 11E39; Secondary 14H05, 16W10
DOI: https://doi.org/10.1090/proc/13413
Published electronically: December 7, 2017
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Abstract: Let $ p$ be an odd prime. Let $ F$ be the function field of a $ p$-adic curve. Let $ A$ be a central simple algebra of period 2 over $ F$ with an involution $ \sigma $. There are known upper bounds for the $ u$-invariant of hermitian forms over $ (A, \sigma )$. In this article we compute the exact values of the $ u$-invariant of hermitian forms over $ (A, \sigma )$.


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Additional Information

Zhengyao Wu
Affiliation: Department of Mathematics and Computer Science, Emory University, 400 Dowman Drive, W401, Atlanta, Georgia 30322
Email: wuzhengyao07@hotmail.com

DOI: https://doi.org/10.1090/proc/13413
Keywords: Hermitian form, $u$-invariant, $p$-adic curve
Received by editor(s): December 23, 2015
Received by editor(s) in revised form: April 7, 2016
Published electronically: December 7, 2017
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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