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 |
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Pages (from-to) | 3145-3163 |
Number of pages | 19 |
Journal | Communications in Algebra |
Volume | 35 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 1 2007 |
Keywords
- Covering
- G-graded
- Koszul
ASJC Scopus subject areas
- Algebra and Number Theory