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Going up of the u-invariant over formally real fields

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Let F be a field of characteristic not 2, and assume that F has finite reduced stability. Let K/F be any finite extension. We prove that if the general u-invariant u(F) is finite, then u(K) is finite.

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References

  1. Bröcker L. (1974). Zur Theorie der quadratischen Formen über formal reellen Körpern. Math. Ann. 210: 233–256, MR 0354549 (50 #7027)

    Article  MATH  MathSciNet  Google Scholar 

  2. Elman R. and Lam T.Y. (1972). Quadratic forms over formally real fields and pythagorean fields. Am. J. Math. 94: 1155–1194, MR 0314878 (47 #3427)

    Article  MATH  MathSciNet  Google Scholar 

  3. Elman R. and Lam T.Y. (1976). Quadratic forms under algebraic extensions. Math. Ann. 219(1): 21–42, MR 0401649 (53 #5476)

    Article  MATH  MathSciNet  Google Scholar 

  4. Elman, R.: Quadratic forms and the u-invariant. III. Conference on Quadratic Forms—1976 (Proc. Conf., Queen’s Univ., Kingston, Ont., 1976), Queen’s Univ., Kingston, Ont., 1977, pp. 422–444. Queen’s Papers in Pure and Appl. Math., No. 46. MR 0491490 (58 #10732)

  5. Leep D.P. (1984). Systems of quadratic forms. J. Reine Angew. Math. 350: 109–116, MR 743536 (85j:11038)

    MATH  MathSciNet  Google Scholar 

  6. Marshall M. (1980). Spaces of orderings, IV. Can. J. Math. 32(3): 603–627, MR 586979 (81m:10035)

    MATH  MathSciNet  Google Scholar 

  7. Marshall M. (1980). The Witt ring of a space of orderings. Trans. Am. Math. Soc. 258(2): 505–521, MR 558187 (81b:10012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Marshall M. (1996). Spaces of orderings and abstract real spectra Lecture Notes in Mathematics, vol. 1636. Springer, Berlin, MR 1438785 (98b:14041)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA, 90095-1555, USA

    Claus Schubert

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  1. Claus Schubert
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Correspondence to Claus Schubert.

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This article is based on part of the author’s Ph.D. thesis, written under the supervision of Richard Elman.

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Schubert, C. Going up of the u-invariant over formally real fields. Math. Ann. 338, 757–765 (2007). https://doi.org/10.1007/s00208-007-0095-1

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  • DOI: https://doi.org/10.1007/s00208-007-0095-1

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