Pawel Gladki, Murray Marshall: Witt equivalence of function fields over global fields,

Submission: 2015, Feb 3

In our work we investigate Witt equivalence of general function fields over global fields. It is proven that for any two such fields K and L the Witt equivalence induces a canonical bijection between Abhyankar valuations on K and L having residue fields not finite of characteristic 2. The main tool used in the proof is a method of constructing valuations due to Arason, Elman and Jacob. Numerous applications are provided, in particular to Witt equivalence of function fields over number fields: it is proven, among other things, that for two number fields k and l the Witt equivalence between the fields k(x_1,…,x_n) and l(x_1,…,x_n) implies that k and l are themselves Witt equivalent and have equal 2-ranks of their ideal class groups.

2010 Mathematics Subject Classification: 11E81, 12J20 (primary), 11E04, 11E12 (secondary)

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