Correspondence and Equivariant Sheaves on P1

2006 ◽  
Vol 6 (3) ◽  
pp. 505-529 ◽  
Author(s):  
A. Kirillov ◽  
Jr. McKay
Keyword(s):  
Equivariant Sheaves

scholarly journals Equivariant sheaves

1999 ◽  
Vol 10 (2-3) ◽  
pp. 399-412 ◽  
Author(s):  
Allen Knutson ◽  
Eric Sharpe
Keyword(s):  
Equivariant Sheaves

scholarly journals The spherical building and regular semisimple elements

1983 ◽  
Vol 27 (3) ◽  
pp. 361-379 ◽  
Author(s):  
G.I. Lehrer
Keyword(s):  
Finite Group ◽  
Finite Field ◽  
Algebraic Group ◽  
Weyl Group ◽  
Rational Points ◽  
Semisimple Element ◽  
Spherical Building ◽  
Reductive Algebraic Group ◽  
Equivariant Sheaves

Let G be a connected reductive algebraic group defined over a finite field k. The finite group G(k) of k-rational points of G acts on the spherical building B(G), a polyhedron which is functorially associated with G. We identify the subspace of points of B(G) fixed by a regular semisimple element s of G(k) topologically as a subspace of a sphere (apartment) in B(G) which depends on an element of the Weyl group which is determined by s. Applications include the derivation of the values of certain characters of G(k) at s by means of Lefschetz theory. The characters considered arise from the action of G(k) on the cohomology of equivariant sheaves over B(G).

scholarly journals CATEGORIFYING RATIONALIZATION

2019 ◽  
Vol 7 ◽  
Author(s):  
CLARK BARWICK ◽  
SAUL GLASMAN ◽  
MARC HOYOIS ◽  
DENIS NARDIN ◽  
JAY SHAH
Keyword(s):  
Grothendieck Group ◽  
Triangulated Category ◽  
Dense Subgroup ◽  
Cantor Space ◽  
Equivariant Sheaves

We construct, for any set of primes $S$ , a triangulated category (in fact a stable $\infty$ -category) whose Grothendieck group is $S^{-1}\mathbf{Z}$ . More generally, for any exact $\infty$ -category $E$ , we construct an exact $\infty$ -category $S^{-1}E$ of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this $\infty$ -category is precisely the result of categorifying division by the primes in $S$ . In particular, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$ .

Equivariant Sheaves and Functors

1994 ◽  
Author(s):  
Joseph Bernstein ◽  
Valery Lunts
Keyword(s):  
Equivariant Sheaves

Moduli of equivariant sheaves and Kronecker–McKay modules

2015 ◽  
Vol 26 (11) ◽  
pp. 1550092 ◽  
Author(s):  
Sanjay Amrutiya ◽  
Umesh Dubey
Keyword(s):  
Finite Group ◽  
Theta Functions ◽  
Moduli Of Sheaves ◽  
A Finite Group ◽  
Equivariant Sheaves

We extend Álvarez-Cónsul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Γ-schemes, for a finite group Γ. We introduce the notion of Kronecker–McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker–McKay modules. Following Álvarez-Cónsul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

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