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

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 $(A,\sigma )$.

12 pages. It merged the published paper and the errata, more typos are fixed