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Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
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TL;DR: In this article, the convolution algebra in the equivariant K-theory of the Hilbert scheme of A2 was shown to be isomorphic to the elliptic Hall algebra and hence to the spherical double affine Hecke algebra of GL∞.
Abstract: In this paper we compute the convolution algebra in the equivariant K-theory of the Hilbert scheme of A2. We show that it is isomorphic to the elliptic Hall algebra and hence to the spherical double affine Hecke algebra of GL∞. We explain this coincidence via the geometric Langlands correspondence for elliptic curves, by relating it also to the convolution algebra in the equivariant K-theory of the commuting variety. We also obtain a few other related results (action of the elliptic Hall algebra on the K-theory of the moduli space of framed torsion free sheaves over P2, virtual fundamental classes, shuffle algebras, …).
103 citations
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01 Jan 1994
TL;DR: Inverse limits of G-toposes: Two examples of group actions on spaces: Topological versus topos-theoretic constructions and Quotient topos of a g-topos, for G of prime order.
Abstract: Real spectrum and real etale site.- Glueing etale and real etale site.- Limit theorems, stalks, and other basic facts.- Some reminders on Weil restrictions.- Real spectrum of X and etale site of .- The fundamental long exact sequence.- Cohomological dimension of X b , I: Reduction to the field case.- Equivariant sheaves for actions of topological groups.- Cohomological dimension of X b , II: The field case.- G-toposes.- Inverse limits of G-toposes: Two examples.- Group actions on spaces: Topological versus topos-theoretic constructions.- Quotient topos of a G-topos, for G of prime order.- Comparison theorems.- Base change theorems.- Constructible sheaves and finiteness theorems.- Cohomology of affine varieties.- Relations to the Zariski topology.- Examples and complements.
103 citations
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TL;DR: In this paper, an explicit group-invariant formula for the Euler- Lagrange equations associated with an invariant variational problem is derived, which relies on a group invariant version of the variational bicomplex induced by a general equivariant moving frame construction.
Abstract: In this paper, we derive an explicit group-invariant formula for the Euler- Lagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest.
102 citations
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TL;DR: In this paper, it was shown that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is etale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group.
Abstract: We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is etale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
101 citations