Raman Parimala

Affiliation: Emory University

Email: parimala@mathcs.emory.edu

Title Of Talk: Isotropy of quadratic forms over function fields of p-adic curves

Abstract: Let K be a field of characteristic not 2. The u-invariant of K, denoted by u(K), is the maximum dimension of anisotropic quadratic forms over K. It remains an open question, whether the finiteness of u(K) implies finiteness of u(K(t)) where K(t) denotes the rational function field in one variable over K. This was an open question even when K = Q_p until a decade ago. In analogy with the positive characteristic local field case, the u-invariant of Q_p(t) was expected to be 8. This was proved to be true for p not equal to 2, by Suresh-Parimala. Whether u(Q_p(t) is finite is still an open question We shall discuss in this lecture the history of the problem and a more recent approach to this problem via certain patching techniques for fields due to Harbater-Hartman-Krashen.

Last update made Thu Feb 19 19:30:17 EST 2009.
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