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The Zariski problem for function fields of quadratic forms


Author: Jack Ohm
Journal: Proc. Amer. Math. Soc. 124 (1996), 1679-1685
MSC (1991): Primary 11E04, 11E81, 12F20
DOI: https://doi.org/10.1090/S0002-9939-96-03238-8
MathSciNet review: 1307553
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Abstract: By `a quadratic function field' is meant the affine function field of a nonsingular quadratic form of dimension $> 2$. What quadratic function fields contain a given quadratic function field $k(P)$? This problem is solved here for quadratic forms $P$ of dimensions 3 and 4, and an application to the Zariski cancellation problem for quadratic function fields is given.


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Additional Information

Jack Ohm
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: mmohm@lsuvax.sncc.lsu.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03238-8
Keywords: Quadratic form, function field, Zariski problem
Received by editor(s): February 14, 1994
Received by editor(s) in revised form: December 9, 1994
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society

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