Witt equivalence of semilocal Dedekind domains in global fields

摘要

We examine a condition for two semilocal Dedekind rings, the fields of fractions of which are global fields, to be Witt equivalent. To solve the problem we generalize the notion of a Hilbert-symbol equivalence introduced in [11] and prove that a Witt equivalence is equivalent to a Hilbert-symbol equivalence. As a result we describe a Witt equivalence in terms of field invariants.