  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 $\tilde{I}$ and a sheaf of Witt rings $\tilde{W}$ in the
obvious way. The Milnor conjecture then relates the associated graded of
$\tilde{W}$ to Milnor K-theory and so allows the classical invariants of a
bilinear space over a field to be extended to our setting using \'etale
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.
