منابع مشابه
Endomorphisms of Deligne-lusztig Varieties
We study some conjectures on the endomorphism algebras of the cohomology of Deligne-Lusztig varieties which are a refinement of those of [BMi].
متن کاملOn the Affineness of Deligne-lusztig Varieties
We prove that the Deligne-Lusztig variety associated to minimal length elements in any δ-conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in [10]. 1.1 Notations. Let k be an algebraic closure of the finite prime field Fp and G be a connected reductive algebraic group over k with an endomorphism F : G → G such that some power F d of F is the Frobenius endo...
متن کاملDimensions of Some Affine Deligne-lusztig Varieties
Let k be a finite field with q elements, and let k̄ be an algebraic closure of k. We consider the field L := k̄((ǫ)) and its subfield F := k((ǫ)). We write σ : x 7→ x for the Frobenius automorphism of k̄/k, and we also regard σ as an automorphism of L/F in the usual way, so that σ( ∑ anǫ ) = ∑ σ(an)ǫ . We write o for the valuation ring k̄[[ǫ]] of L. Let G be a split connected reductive group over k...
متن کاملOn the Connectedness of Deligne-lusztig Varieties
We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.
متن کاملDimensions of Some Affine Deligne-lusztig Varieties Les Dimensions De Certaines Variétés De Deligne-lusztig Affines
This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties Xμ(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2006
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000009260