Abstract
For a finite group G and a field k of prime characteristic, we study certain pure injective kG-modules in terms of the spectrum of the group cohomology ring H* (G, k). For instance, we construct a map from the projective variety Proj (H* (G, k)) to the Ziegler spectrum of indecomposable pure injective kG-modules. We identify the module corresponding to a generic point for a component of the variety; it is generic in the sense of Crawley-Boevey and closely related to a certain Rickard idempotent module. We include also a complete classification of all kG-modules which arise as a direct summand of a (possibly infinite) product of syzygies of the trivial module k.
| Original language | English |
|---|---|
| Pages (from-to) | 23-51 |
| Number of pages | 28 |
| Journal | Journal für die reine und angewandte Mathematik |
| Volume | 542 |
| DOIs | |
| Publication status | Published - 2002 |
Keywords
- INFINITELY GENERATED MODULES
- PHANTOM MAPS
- CATEGORY
- COMPLEXITY
- VARIETIES
Cite this
Pure injectives and the spectrum of the cohomology ring of a finite group. / Benson, David John; Krause, H.
In: Journal für die reine und angewandte Mathematik, Vol. 542, 2002, p. 23-51.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Pure injectives and the spectrum of the cohomology ring of a finite group
AU - Benson, David John
AU - Krause, H.
PY - 2002
Y1 - 2002
N2 - For a finite group G and a field k of prime characteristic, we study certain pure injective kG-modules in terms of the spectrum of the group cohomology ring H* (G, k). For instance, we construct a map from the projective variety Proj (H* (G, k)) to the Ziegler spectrum of indecomposable pure injective kG-modules. We identify the module corresponding to a generic point for a component of the variety; it is generic in the sense of Crawley-Boevey and closely related to a certain Rickard idempotent module. We include also a complete classification of all kG-modules which arise as a direct summand of a (possibly infinite) product of syzygies of the trivial module k.
AB - For a finite group G and a field k of prime characteristic, we study certain pure injective kG-modules in terms of the spectrum of the group cohomology ring H* (G, k). For instance, we construct a map from the projective variety Proj (H* (G, k)) to the Ziegler spectrum of indecomposable pure injective kG-modules. We identify the module corresponding to a generic point for a component of the variety; it is generic in the sense of Crawley-Boevey and closely related to a certain Rickard idempotent module. We include also a complete classification of all kG-modules which arise as a direct summand of a (possibly infinite) product of syzygies of the trivial module k.
KW - INFINITELY GENERATED MODULES
KW - PHANTOM MAPS
KW - CATEGORY
KW - COMPLEXITY
KW - VARIETIES
U2 - 10.1515/crll.2002.008
DO - 10.1515/crll.2002.008
M3 - Article
VL - 542
SP - 23
EP - 51
JO - Journal für die reine und angewandte Mathematik
JF - Journal für die reine und angewandte Mathematik
SN - 0075-4102
ER -