Local cohomology and support for triangulated categories

Dave Benson; Srikanth B. Iyengar; Henning Krause

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 4, page 575-621
  • ISSN: 0012-9593

Abstract

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We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects, the triangulated support and cohomological support of which differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.

How to cite

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Benson, Dave, Iyengar, Srikanth B., and Krause, Henning. "Local cohomology and support for triangulated categories." Annales scientifiques de l'École Normale Supérieure 41.4 (2008): 575-621. <http://eudml.org/doc/272216>.

@article{Benson2008,
abstract = {We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects, the triangulated support and cohomological support of which differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.},
author = {Benson, Dave, Iyengar, Srikanth B., Krause, Henning},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {local cohomology; support; triangulated category; complete intersection},
language = {eng},
number = {4},
pages = {575-621},
publisher = {Société mathématique de France},
title = {Local cohomology and support for triangulated categories},
url = {http://eudml.org/doc/272216},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Benson, Dave
AU - Iyengar, Srikanth B.
AU - Krause, Henning
TI - Local cohomology and support for triangulated categories
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 4
SP - 575
EP - 621
AB - We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects, the triangulated support and cohomological support of which differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.
LA - eng
KW - local cohomology; support; triangulated category; complete intersection
UR - http://eudml.org/doc/272216
ER -

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