The $u$-invariant of the function fields of $p$-adic curves


The $u$-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the $u$-invariant of function fields of $p$-adic curves is $8$. In this paper, we answer this question in the affirmative for function fields of nondyadic $p$-adic curves.


Raman Parimala

Department of Mathematics and Computer Science
Emory University
400 Dowman Drive
Atlanta, Georgia 30322
United States

V. Suresh

Department of Mathematics and Statistics
University of Hyderabad
Hyderabad - 500046