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2022 | OriginalPaper | Chapter

Fourier-Sato Transform on Hyperplane Arrangements

Authors : Michael Finkelberg, Mikhail Kapranov, Vadim Schechtman

Published in: Representation Theory and Algebraic Geometry

Publisher: Springer International Publishing

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Abstract

The theory of perverse sheaves can be said to provide an interpolation between homology and cohomology (or to mix them in a self-dual way). Since homology, sheaf-theoretically, can be understood as cohomology with compact support, interesting operations on perverse sheaves usually combine the functors of the types f! and f or, dually, the functors of the types f! and f in the classical formalism of Grothendieck.

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Footnotes
1
The notation ⊕ here and below means direct sum of vector bundles, i.e., fiber product over N.
 
Literature
[Ar]
go back to reference J. Arthur. An introduction to the trace formula. In: “Harmonic Analysis, Trace Formula and Schimura Varieties” (J. Arthur, D. Ellwood, R. Kottwitz Eds.) Clay Math. Proceedings4, Amer. Math. Soc. (2005) 3–263. J. Arthur. An introduction to the trace formula. In: “Harmonic Analysis, Trace Formula and Schimura Varieties” (J. Arthur, D. Ellwood, R. Kottwitz Eds.) Clay Math. Proceedings4, Amer. Math. Soc. (2005) 3–263.
[Be]
go back to reference A. Beilinson. How to glue perverse sheaves. In: K-theory, arithmetic and geometry (Moscow, 1984), Lecture Notes in Math.1289, Springer-Verlag, (1987) 42–51. A. Beilinson. How to glue perverse sheaves. In: K-theory, arithmetic and geometry (Moscow, 1984), Lecture Notes in Math.1289, Springer-Verlag, (1987) 42–51.
[BBD]
go back to reference A. Beilinson, J. Bernstein, P. Deligne. Faisceaux pervers. Astérisque100 (1983). A. Beilinson, J. Bernstein, P. Deligne. Faisceaux pervers. Astérisque100 (1983).
[BFS]
go back to reference R. Bezrukavnikov, M. Finkelberg, V. Schechtman. Factorizable sheaves and quantum groups. Lecture Notes in Math.1691, Springer-Verlag, (1998). R. Bezrukavnikov, M. Finkelberg, V. Schechtman. Factorizable sheaves and quantum groups. Lecture Notes in Math.1691, Springer-Verlag, (1998).
[Br]
[De]
go back to reference P. Deligne, Le formalisme des cycles évanescents. SGA 7, Exp. 13, 14 Lecture Notes in Math.340, Springer-Verlag (1973). P. Deligne, Le formalisme des cycles évanescents. SGA 7, Exp. 13, 14 Lecture Notes in Math.340, Springer-Verlag (1973).
[FL]
go back to reference T. Finis, E. Lapid. On the spectral side of the Arthur’s trace formula—combinatorial setup. Ann. Math.174 (2011) 197–223.MathSciNetCrossRef T. Finis, E. Lapid. On the spectral side of the Arthur’s trace formula—combinatorial setup. Ann. Math.174 (2011) 197–223.MathSciNetCrossRef
[FS]
go back to reference M. Finkelberg, V. Schechtman. Microlocal approach to Lusztig’s symmetries. arXiv:1401.5885. M. Finkelberg, V. Schechtman. Microlocal approach to Lusztig’s symmetries. arXiv:1401.5885.
[KS1]
[KS2]
go back to reference M. Kashiwara, P. Schapira, Sheaves on Manifolds. Grundlehren der Mathematischen Wissenschaften292, Springer-Verlag, (1990). M. Kashiwara, P. Schapira, Sheaves on Manifolds. Grundlehren der Mathematischen Wissenschaften292, Springer-Verlag, (1990).
[L]
go back to reference Y. Laurent. Théorie de la Deuxième Microlocalization dans le Domaine Complexe. Progress in Math.53, Birkhäuser, Boston, (1985). Y. Laurent. Théorie de la Deuxième Microlocalization dans le Domaine Complexe. Progress in Math.53, Birkhäuser, Boston, (1985).
[MV]
[ST]
go back to reference P. Schapira, K. Takeuchi. Déformation binormale et bispecialization. C. R. Acad. Sci.319 (1994) 707–712.MathSciNetMATH P. Schapira, K. Takeuchi. Déformation binormale et bispecialization. C. R. Acad. Sci.319 (1994) 707–712.MathSciNetMATH
[V]
go back to reference A. N. Varchenko, Combinatorics and topology of the arrangement of affine hyperplanes in the real space. Funct. Anal. Appl.21 (1987) 11–22.MathSciNetCrossRef A. N. Varchenko, Combinatorics and topology of the arrangement of affine hyperplanes in the real space. Funct. Anal. Appl.21 (1987) 11–22.MathSciNetCrossRef
Metadata
Title
Fourier-Sato Transform on Hyperplane Arrangements
Authors
Michael Finkelberg
Mikhail Kapranov
Vadim Schechtman
Copyright Year
2022
DOI
https://doi.org/10.1007/978-3-030-82007-7_4

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