Witt equivalence of function fields over global fields
Rings and Algebras
2016-02-01 v2
Abstract
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.
Cite
@article{arxiv.1502.00830,
title = {Witt equivalence of function fields over global fields},
author = {Pawel Gladki and Murray Marshall},
journal= {arXiv preprint arXiv:1502.00830},
year = {2016}
}