SUFFICIENTLY GENERIC ORTHOGONAL GRASSMANNIANS 1 ...

• exposé

SUFFICIENTLY GENERIC ORTHOGONAL GRASSMANNIANS NIKITA A. KARPENKO Abstract. We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer satisfying 1 ≤ i ≤ (dim q)/2). Assume that q is sufficiently generic in the following sense: the degree of each closed point on Q is divisible by 2i and the Witt index of q over the function field of Q is equal to i.

• smooth projective varieties
• motive
• projective bundle
• direct sum of indecomposable motives
• word for word
• word by word
• fp
• coefficients
• dimension
• variety
• field