# zbMATH — the first resource for mathematics

Perverse sheaves on affine Grassmannians and Langlands duality. (English) Zbl 0987.14015
The paper outlines the construction of the Langlands duality, i.e. the equivalent of the category of $$k$$-representations of the Langlands dual group $$^LG$$ and the category of perverse sheaves with coefficients in $$\mathbb{K}$$ on the affine Grassmannian associated in $$G$$ for a complex algebraic reductive group $$G$$. The result for $$\mathbb{K}$$ the field of complex numbers is due to V. Ginzburg (alg-geom/9511007). The authors generalize it to any commutative ring $$\mathbb{K}$$, and claim new proofs for some crucial steps of the complex case, but the text only outlines the constructions and announces the results.

##### MSC:
 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14M15 Grassmannians, Schubert varieties, flag manifolds 20G05 Representation theory for linear algebraic groups 18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
Full Text: