Koszul duality and semisimplicity of Frobenius

Pramod N. Achar[1]; Simon Riche[2]

  • [1] Department of Mathematics Louisiana State University Baton Rouge, LA 70803 USA
  • [2] Clermont Université, Université Blaise Pascal, Laboratoire de Mathématiques, BP 10448, F-63000 Clermont-Ferrand. CNRS, UMR 6620, Laboratoire de Mathématiques, F-63177 Aubière.

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 4, page 1511-1612
  • ISSN: 0373-0956

Abstract

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A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of ℓ -adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.

How to cite

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Achar, Pramod N., and Riche, Simon. "Koszul duality and semisimplicity of Frobenius." Annales de l’institut Fourier 63.4 (2013): 1511-1612. <http://eudml.org/doc/275579>.

@article{Achar2013,
abstract = {A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of $\ell $-adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.},
affiliation = {Department of Mathematics Louisiana State University Baton Rouge, LA 70803 USA; Clermont Université, Université Blaise Pascal, Laboratoire de Mathématiques, BP 10448, F-63000 Clermont-Ferrand. CNRS, UMR 6620, Laboratoire de Mathématiques, F-63177 Aubière.},
author = {Achar, Pramod N., Riche, Simon},
journal = {Annales de l’institut Fourier},
keywords = {Koszul duality; perverse sheaves; flag variety},
language = {eng},
number = {4},
pages = {1511-1612},
publisher = {Association des Annales de l’institut Fourier},
title = {Koszul duality and semisimplicity of Frobenius},
url = {http://eudml.org/doc/275579},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Achar, Pramod N.
AU - Riche, Simon
TI - Koszul duality and semisimplicity of Frobenius
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 4
SP - 1511
EP - 1612
AB - A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of $\ell $-adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.
LA - eng
KW - Koszul duality; perverse sheaves; flag variety
UR - http://eudml.org/doc/275579
ER -

References

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