The Zariski problem for function fields of quadratic forms
Author:
Jack Ohm
Journal:
Proc. Amer. Math. Soc. 124 (1996), 16791685
MSC (1991):
Primary 11E04, 11E81, 12F20
MathSciNet review:
1307553
Fulltext PDF Free Access
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Abstract: By `a quadratic function field' is meant the affine function field of a nonsingular quadratic form of dimension . What quadratic function fields contain a given quadratic function field ? This problem is solved here for quadratic forms of dimensions 3 and 4, and an application to the Zariski cancellation problem for quadratic function fields is given.
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, Fields of uinvariant 6 after A. Merkurjev, Isarel Math. Conf. Proc., Ring Theory 1989 (in honor of S.A. Amitsur) (L. Rowen, ed.), vol. I, Weizmann Science Press, Jerusalem, 1989, pp. 1231.
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 H. Ahmad and J. Ohm, Function fields of Pfister neighbors, J. Algebra 178 (1995), 653664.
 [B]
 A. Beauville, J.L. ColliotThlne, J.J. Sansuc, and Sir Peter SwinnertonDyer, Varietes stablement rationnelles non rationnelles, Annals of Math. 121 (1986), 283318. MR 86m:14009
 [H1]
 D. Hoffmann, Isotropy of 5dimensional Quadratic forms over the function field of a quadric, preprint.
 [H2]
 , On 6dimensional quadratic forms isotropic over the function field of a quadric, Comm. in Algebra 22(6) (1994), 19992014. CMP 94:10
 [H3]
 , Minimal quadratic forms and function fields of quadratic forms, preprint.
 [K]
 M. Knebusch, Generic splitting of quadratic forms I, Proc. London Math. Soc. 33 (1976), 6593; II Proc. London Math. Soc., vol. 34, 1977, pp. 131. MR 55:379
 [L]
 T.Y. Lam, The algebraic theory of quadratic forms, Benjamin, Reading, Mass., 1980. MR 83d:10022
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 , Fields of uinvariant 6 after A. Merkurjev, Isarel Math. Conf. Proc., Ring Theory 1989 (in honor of S.A. Amitsur) (L. Rowen, ed.), vol. I, Weizmann Science Press, Jerusalem, 1989, pp. 1231.
 [O1]
 J. Ohm, On subfields of rational function fields, Arch. Math 42 (1984), 136138. MR 86h:12007
 [O2]
 , On ruled fields, Sem. de theorie des nombres, Bordeaux 1, Serie 2 1 (1989), 2750. MR 91g:12006
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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:
http://dx.doi.org/10.1090/S0002993996032388
PII:
S 00029939(96)032388
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
