Hyperbolic localization of intersection cohomology

By Tom Braden. 2002

164 citations recorded by the source corpus.

AbstractFor a normal variety X defined over an algebraically closed field with an action of the multiplicative group T = Gm, we consider the "hyperbolic localization" functor Db(X) → Db(XT), which localizes using closed supports in the directions flowing into the fixed points, and compact supports in the directions flowing out. We show that the hyperbolic localization of the intersection cohomology sheaf is a direct sum of intersection cohomology sheaves.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/31a44ddb41403f4eb70494b6c758fb699bba7647

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Perverse sheaves on real loop Grassmannians (2002, background): “m [GM93, Proposition 9.2]. Alternatively, it follows immediately by checking that the arguments of [Bra02, Theorem 1 and Lemma 5] hold in this setting, for which see Remark (4) of the introduction of [Bra02]. (To apply the arguments, note that by the embedding of Section 4.4, we may work on an ambie”
Geometry of canonical bases and mirror symmetry (2013, background): “Combining Theorem 1 and Section 3 of [7], we have the following result, which implies (143).”
Parity Sheaves (2009, background): “In the terminology of Braden [Bra03], this is an example of a hyperbolic localisation.”
Perverse sheaves over real hyperplane arrangements (2014, background): “) Extending the terminology of [8], we will call the perverse sheaf k∗j!F [d] the hyperbolic restriction of F to LC.”
Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties (2010, background): “But this is shown in [Spr82] (see also [Bra03] for another account of this argument).”
ON A THEOREM OF BRADEN (2013, background): “m. ON A THEOREM OF BRADEN 3 are both deﬁned 3 on objects of D-mod(Z)G m -mon and we have a canonical isomorphism (0.2) (i+)•◦(p+)!| D-mod(Z)Gm-mon ≃(i −)! ◦(p−)•| D-mod(Z)Gm-mon . 0.1.3. In his paper [Br], T. Braden formulated and proved his theorem assuming that Z is a normal algebraic variety. Alt”
The test function conjecture for parahoric local models (2018, methodology): “ively) Gm-equivariant if there exists an isomorphism 44 T.J.HAINES AND T.RICHARZ p ∗A≃aAin Db c(G m,S× SX,Q¯ℓ), where p(resp. a) denotes the projection (resp. action) G × X→X. Following the method in [Br03] for normal varieties over algebraically closed ﬁelds, it is shown in [Ri, Thm 2.6] that the t”