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Exact functors on perverse coherent sheaves

Published online by Cambridge University Press:  04 May 2015

Clemens Koppensteiner*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Rd, Evanston, IL 60208, USA email [email protected]
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Abstract

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Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$. These subvarieties $Z$ are analogs of Lagrangians in the symplectic case.

Type
Research Article
Copyright
© The Author 2015 

References

Arinkin, D. and Bezrukavnikov, R., Perverse coherent sheaves, Mosc. Math. J. 10 (2010), 329.CrossRefGoogle Scholar
Beauville, A., Symplectic singularities, Invent. Math. 139 (2000), 541549.CrossRefGoogle Scholar
Bezrukavnikov, R., Perverse coherent sheaves (after Deligne), Preprint (2000), arXiv:math/0005152.Google Scholar
Brodmann, M. P. and Sharp, R. Y., Local cohomology: an algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics, vol. 60 (Cambridge University Press, Cambridge, 1998), doi:10.1017/CBO9780511629204.Google Scholar
Hartshorne, R., Residues and duality, Lecture Notes in Mathematics, vol. 20 (Springer, Berlin, 1966).Google Scholar
Kashiwara, M., t-structures on the derived categories of holonomic D-modules and coherent 𝓞-modules, Mosc. Math. J. 4 (2004), 847868.CrossRefGoogle Scholar
Kashiwara, M. and Schapira, P., Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften, vol. 292 (Springer, Berlin, 1994).Google Scholar
Mirkovi, I. and Vilonen, K., Geometric Langlands duality and representations of algebraic groups over commutative rings, Ann. of Math. (2) 166 (2007), 95143; doi:10.4007/annals.2007.166.95.CrossRefGoogle Scholar
Grothendieck, A. and Raynaud, M., Cohomologie locale des faisceaux co-hérents et théorémes de Lefschetz locaux et globaux (SGA2), Documents Mathématiques, vol. 4 (Société Mathématique de France, Paris, 2005); arXiv:math/0511279; MR 2171939.Google Scholar
Williamson, G., Vanishing of !-restriction of constructible sheaves, MathOverflow (2013), http://mathoverflow.net/a/129244.Google Scholar