alexander.vishik@nottingham.ac.uk

Submission: 2009, May 24, revised: 2009, June 17

In this article we show that connections in the motives of excellent quadrics are minimal for anisotropic quadrics of given dimension. This provides severe restrictions for the Motivic Decomposition Type invariant. As a corollary we estimate from below the rank of indecomposable direct summand in the motive of a quadric in terms of its dimension. This generalises the well-known binary motive Theorem. Moreover, we have the description of Tate-motives involved. As a corollary one gets another proof of Karpenko's Theorem on the value of the first higher Witt index. But also other new relations among the higher Witt indices follow.

2000 Mathematics Subject Classification: 11E04, 14C15, 14C25

Keywords and Phrases: Quadrics, Motives, Chow groups, Steenrod operations, Algebraic Cobordism

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