Local-global principle for Witt equivalence of function fields over global fields
Tom 91 / 2002
Colloquium Mathematicum 91 (2002), 293-302
MSC: Primary 11E81; Secondary 11G30, 14H05.
DOI: 10.4064/cm91-2-8
Streszczenie
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies Witt equivalence of their fields of constants. We also discuss the converse of this implication.
