2015/02/03 by Pawel Gladki, Gladki, Pawel, Murray Marshall +1 · 1 citation
Mathematics · #11E04 #11E12 (secondary) #11E81 #12J20 (primary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:11E04 #msc:11E12 #msc:11E81 #msc:12J20
paper · pdf · doi:10.48550/arxiv.1502.00830
arxiv created 2016/01/29 · arxiv updated 2016/02/01
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(x1,...,xn) and l(x1,...,xn) implies that k and l are themselves Witt equivalent and have equal 2-ranks of their ideal class groups.