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The Zariski problem for function fields of quadratic forms

Author(s): Jack Ohm
Journal: Proc. Amer. Math. Soc. 124 (1996), 1679-1685.
MSC (1991): Primary 11E04, 11E81, 12F20
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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.

References:

[AO]
H. Ahmad and J. Ohm, Function fields of Pfister neighbors, J. Algebra 178 (1995), 653--664.

[B]
A. Beauville, J.-L. Colliot-Th$\acute e$l$\grave e$ne, J.-J. Sansuc, and Sir Peter Swinnerton-Dyer, Varietes stablement rationnelles non rationnelles, Annals of Math. 121 (1986), 283--318. MR 86m:14009

[H1]
D. Hoffmann, Isotropy of 5-dimensional Quadratic forms over the function field of a quadric, preprint.

[H2]
------, On 6-dimensional quadratic forms isotropic over the function field of a quadric, Comm. in Algebra 22(6) (1994), 1999-2014. 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), 65-93; II Proc. London Math. Soc., vol. 34, 1977, pp. 1--31. MR 55:379

[L]
T.Y. Lam, The algebraic theory of quadratic forms, Benjamin, Reading, Mass., 1980. MR 83d:10022

[L2]
------, Fields of u-invariant 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. 12--31.

[O1]
J. Ohm, On subfields of rational function fields, Arch. Math 42 (1984), 136-138. MR 86h:12007

[O2]
------, On ruled fields, Sem. de theorie des nombres, Bordeaux 1, Serie 2 1 (1989), 27-50. MR 91g:12006

[O3]
------, Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski, Algebraic geometry and its applications (C. Bajaj, ed.), Springer-Verlag, 1994, pp. 333--363. MR 95c:12010

[W]
A. Wadsworth, Similarity of quadratic forms and isomorphism of their function fields, Trans. Amer. Math. Soc. 208 (1975), 352--358. MR 51:12702

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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: 10.1090/S0002-9939-96-03238-8
PII: S 0002-9939(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
Copyright of article: Copyright 1996, American Mathematical Society

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