Abstract
A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand- Gelfand that states the existence of an equivalence of triangulated categories: grΛ ≅ Db(Coh ℙn), where grΛ denotes the stable category of finitely generated graded modules over the n + 1 exterior algebra and Db(Coh ℙn) is the derived category of bounded complexes of coherent sheaves on projective space ℙn. Generalizations of this result were obtained in Martínez-Villa and Saorín (2004) and from a different point of view, the theorem has been extended by Yanagawa (2004) to ℤn-graded modules over the polynomial algebra. This generalization has important applications in combinatorial commutative algebra. The aim of the article is to extend the results of Martínez-Villa and Saorín (2004) to group graded algebras in order to obtain a generalization of Yanagawa's results having in mind the application to other settings (Geigle and Lenzing, 1987).
| Original language | English |
|---|---|
| Pages (from-to) | 3145-3163 |
| Number of pages | 19 |
| Journal | Communications in Algebra |
| Volume | 35 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Oct 2007 |
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Keywords
- Covering
- G-graded
- Koszul
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
On a group graded version of BGG. / Green, E. L.; Martínez-Villa, R.; Yoshino, Yuji.
In: Communications in Algebra, Vol. 35, No. 10, 10.2007, p. 3145-3163.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On a group graded version of BGG
AU - Green, E. L.
AU - Martínez-Villa, R.
AU - Yoshino, Yuji
PY - 2007/10
Y1 - 2007/10
N2 - A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand- Gelfand that states the existence of an equivalence of triangulated categories: grΛ ≅ Db(Coh ℙn), where grΛ denotes the stable category of finitely generated graded modules over the n + 1 exterior algebra and Db(Coh ℙn) is the derived category of bounded complexes of coherent sheaves on projective space ℙn. Generalizations of this result were obtained in Martínez-Villa and Saorín (2004) and from a different point of view, the theorem has been extended by Yanagawa (2004) to ℤn-graded modules over the polynomial algebra. This generalization has important applications in combinatorial commutative algebra. The aim of the article is to extend the results of Martínez-Villa and Saorín (2004) to group graded algebras in order to obtain a generalization of Yanagawa's results having in mind the application to other settings (Geigle and Lenzing, 1987).
AB - A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand- Gelfand that states the existence of an equivalence of triangulated categories: grΛ ≅ Db(Coh ℙn), where grΛ denotes the stable category of finitely generated graded modules over the n + 1 exterior algebra and Db(Coh ℙn) is the derived category of bounded complexes of coherent sheaves on projective space ℙn. Generalizations of this result were obtained in Martínez-Villa and Saorín (2004) and from a different point of view, the theorem has been extended by Yanagawa (2004) to ℤn-graded modules over the polynomial algebra. This generalization has important applications in combinatorial commutative algebra. The aim of the article is to extend the results of Martínez-Villa and Saorín (2004) to group graded algebras in order to obtain a generalization of Yanagawa's results having in mind the application to other settings (Geigle and Lenzing, 1987).
KW - Covering
KW - G-graded
KW - Koszul
UR - http://www.scopus.com/inward/record.url?scp=34848827908&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34848827908&partnerID=8YFLogxK
U2 - 10.1080/00914030701409825
DO - 10.1080/00914030701409825
M3 - Article
AN - SCOPUS:34848827908
VL - 35
SP - 3145
EP - 3163
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 10
ER -