# Thick subcategories of the stable module category

D. Benson; Jon Carlson; Jeremy Rickard

Fundamenta Mathematicae (1997)

- Volume: 153, Issue: 1, page 59-80
- ISSN: 0016-2736

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topBenson, D., Carlson, Jon, and Rickard, Jeremy. "Thick subcategories of the stable module category." Fundamenta Mathematicae 153.1 (1997): 59-80. <http://eudml.org/doc/212215>.

@article{Benson1997,

abstract = {We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated on each nonzero closed homogeneous subvariety of the nucleus.},

author = {Benson, D., Carlson, Jon, Rickard, Jeremy},

journal = {Fundamenta Mathematicae},

keywords = {triangulated categories; stable module categories; thick subcategories; varieties of modules; idempotent modules; nucleus; principal blocks; finite groups; finitely generated modules},

language = {eng},

number = {1},

pages = {59-80},

title = {Thick subcategories of the stable module category},

url = {http://eudml.org/doc/212215},

volume = {153},

year = {1997},

}

TY - JOUR

AU - Benson, D.

AU - Carlson, Jon

AU - Rickard, Jeremy

TI - Thick subcategories of the stable module category

JO - Fundamenta Mathematicae

PY - 1997

VL - 153

IS - 1

SP - 59

EP - 80

AB - We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated on each nonzero closed homogeneous subvariety of the nucleus.

LA - eng

KW - triangulated categories; stable module categories; thick subcategories; varieties of modules; idempotent modules; nucleus; principal blocks; finite groups; finitely generated modules

UR - http://eudml.org/doc/212215

ER -

## References

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