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On the u-invariant of hermitian forms

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Abstract

Let K be a field of characteristic not 2 and A a central simple algebra with an involution σ. A result of Mahmoudi provides an upper bound for the u-invariants of hermitian forms and skew-hermitian forms over (A, σ) in terms of the u-invariant of K. In this paper we give a different upper bound when A is a tensor product of quaternion algebras and σ is a the tensor product of canonical involutions. We also show that our bounds are sharper than those of Mahmoudi.

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References

  1. Bayer-Fluckiger E and Parimala R, Galois cohomology of the classical groups over fields of cohomological dimension ≤ 2, Invent. Math. 122 (1995) 195–229

    Article  MathSciNet  MATH  Google Scholar 

  2. Knus M-A, Quadratic and Hermitian Forms over Rings, Grundlehren der Math. Wiss (1991) (New York: Springer-Verlag, Berlin-Heidelberg) p. 294

  3. Mahmoudi M G, Hermitian forms and the u-invariant, Manu. Math. 116(4) (2005) 493–516

    Article  MathSciNet  MATH  Google Scholar 

  4. Parimala R and Preeti R, Hasse principle for classical groups over function field of curves over number fields, J. Number Theory 101 (2003) 151–184

    Article  MathSciNet  MATH  Google Scholar 

  5. Parimala R and Suresh V, The u-invariant of the function fields of p-adic curves, Ann. Math. 172(2) (2010) 1391–1405

    Article  MathSciNet  MATH  Google Scholar 

  6. Saltman D, Division algebras over p-adic curves, J. Ramanujan Math. Soc. 12 (1997) 2547

    MathSciNet  Google Scholar 

  7. Scharlau W, Quadratic and Hermitian Forms, Grundlehren der Math. Wiss (1985) (Berlin, Heidelberg, New York) p. 270

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  1. Department of Mathematics and Statistics, University of Hyderabad, Gahcibowli, Hyderabad, 500 046, India

    SUDEEP S PARIHAR & V SURESH

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  1. SUDEEP S PARIHAR
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  2. V SURESH
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Correspondence to V SURESH.

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PARIHAR, S.S., SURESH, V. On the u-invariant of hermitian forms. Proc Math Sci 123, 303–313 (2013). https://doi.org/10.1007/s12044-013-0131-x

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  • DOI: https://doi.org/10.1007/s12044-013-0131-x

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