Buildings, spiders, and geometric Satake
نویسندگان
چکیده
منابع مشابه
Twisted Geometric Satake Equivalence
Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → Gm → E → G(F) → 1, any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN (k) → Q ∗ l (under some assumption on the characteristic of k). Consider the category of G(O)biinvariant perverse sheaves on E wi...
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For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...
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Abstract. For a split reductive group scheme Ǧ over a commutative ring k with Weyl group W , there is an important functor Rep(Ǧ, k) → Rep(W, k) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dua...
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We endow the set of lattices in Qp with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
متن کاملBruhat-tits Theory from Berkovich’s Point of View. Ii. Satake Compactifications of Buildings
In the paper Bruhat-Tits theory from Berkovich’s point of view. I — Realizations and compactifications of buildings, we investigated various realizations of the Bruhat-Tits building B(G,k) of a connected and reductive linear algebraic group G over a non-Archimedean field k in the framework of V. Berkovich’s non-Archimedean analytic geometry. We studied in detail the compactifications of the bui...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2013
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x13007136