Abstract
We prove Hoffmann’s conjecture determining the possible values of the first Witt index of anisotropic quadratic forms of any given dimension. The proof makes use of the Steenrod type operations on the modulo 2 Chow groups constructed by P. Brosnan.
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References
Brosnan, P.: Steenrod Operations in Chow Theory. Trans. Am. Math. Soc. To appear
Eddidin, D., Graham, W.: Equivariant intersection theory. Invent. Math. 131, 595–634 (1998)
Fulton, W.: Intersection Theory. Berlin: Springer 1984
Hoffmann, D.: Isotropy of quadratic forms over the function field of a quadric. Math. Z. 220, 461–476 (1995)
Hoffmann, D.: Splitting patterns and invariants of quadratic forms. Math. Nachr. 190, 149–168 (1998)
Izhboldin, O.T.: Virtual Pfister neighbors and first Witt index. Preprint 2000
Karpenko, N.A.: On anisotropy of orthogonal involutions. J. Ramanujan Math. Soc. 15, 1–22 (2000)
Knebusch, M.: Generic splitting of quadratic forms, I. Proc. Lond. Math. Soc., III. Ser. 33, 65–93 (1976)
Vishik, A.: Direct summands in the motives of quadrics. Preprint 1999
Vishik, A.: Splitting patterns of small-dimensional forms. Preprint 2002
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Mathematics Subject Classification (2000)
11E04, 14C25
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Karpenko, N. On the first Witt index of quadratic forms. Invent. math. 153, 455–462 (2003). https://doi.org/10.1007/s00222-003-0294-7
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DOI: https://doi.org/10.1007/s00222-003-0294-7