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In this work, we present a generalization to varieties and sheaves of thefundamental ideal of the Witt ring of a field by defining a sheaf offundamental ideals $\tilde{I}$ and a sheaf of Witt rings $\tilde{W}$ in theobvious way. The Milnor conjecture then relates the associated graded of$\tilde{W}$ to Milnor K-theory and so allows the classical invariants of abilinear space over a field to be extended to our setting using \'etalecohomology. As an application of these results, we calculate the Witt ring of asmooth curve with good reduction over a non-dyadic local field.

The Witt Ring of a Curve with Good Reduction over a Non-dyadic Local Field