The Witt ring of a curve with good reduction over a non-dyadic local field

Abstract

In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals I˜ and a sheaf of Witt rings W˜ in the obvious way. The Milnor conjecture then relates the associated graded of W˜ to Milnor K-theory and so allows the classical invariants of a bilinear space over a field to be extended to our setting using étale cohomology. As an application of these results, we calculate the Witt ring of a smooth curve with good reduction over a non-dyadic local field.