Local-global principle for Witt equivalence of function fields over global fields

Przemyslaw Koprowski

Colloquium Mathematicae (2002)

  • Volume: 91, Issue: 2, page 293-302
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Przemyslaw Koprowski. "Local-global principle for Witt equivalence of function fields over global fields." Colloquium Mathematicae 91.2 (2002): 293-302. <http://eudml.org/doc/283826>.

@article{PrzemyslawKoprowski2002,
abstract = {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.},
author = {Przemyslaw Koprowski},
journal = {Colloquium Mathematicae},
keywords = {isomorphism of Witt rings; Witt equivalence of fields; global field; algebraic function field},
language = {eng},
number = {2},
pages = {293-302},
title = {Local-global principle for Witt equivalence of function fields over global fields},
url = {http://eudml.org/doc/283826},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Przemyslaw Koprowski
TI - Local-global principle for Witt equivalence of function fields over global fields
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 2
SP - 293
EP - 302
AB - 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.
LA - eng
KW - isomorphism of Witt rings; Witt equivalence of fields; global field; algebraic function field
UR - http://eudml.org/doc/283826
ER -

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