论文信息 - Amplitude inequalities for Differential Graded modules

Amplitude inequalities for Differential Graded modules

Abstract The amplitude of a Differential Graded module M is defined in terms of its homology H(M) by ampM = sup{i | H i (M) ≠ 0} – inf{i | H i (M) ≠ 0}. The main result of this paper is that if R is a sufficiently nice local chain Differential Graded algebra with amp R < ∞, then each compact Differential Graded R-module M with non-zero homology satisfies amp M ≥ amp R.

Peter Jørgensen

[1] Peter Jørgensen,et al. Homological properties of cochain Differential Graded algebras , 2008, 0801.1581.

[2] Karsten Schmidt. Auslander-Reiten theory for simply connected differential graded algebras , 2008, 0801.0651.

[3] S. Iyengar,et al. Dualizing Differential Graded Modules and Gorenstein Differential Graded Algebras , 2003 .

[4] Peter Jørgensen,et al. Homological identities for differential graded algebras , 2003 .

[5] J. R. G. Rozas,et al. Exact and Semisimple Differential Graded Algebras , 2002 .

[6] Peter Jørgensen. Non‐Commutative Graded Homological Identities , 1998 .

[7] L. L. Avramov,et al. Cohen–Macaulay Properties of Ring Homomorphisms , 1998 .

[8] S. Iyengar. Free Resolutions and Change of Rings , 1997 .

[9] I. Kríz,et al. Operads, algebras, modules and motives , 2018, Astérisque.

[10] Bernhard Keller,et al. Deriving DG categories , 1994 .

[11] B. Keller. A remark on tilting theory and DG algebras , 1993 .

[12] Miles Reid,et al. Commutative Ring Theory , 1989 .

[13] H. Foxby. Bounded complexes of flat modules , 1979 .

[14] B. Iversen. Amplitude inequalities for complexes , 1977 .

[15] R. Hartshorne. Residues and Duality: Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963 /64 , 1966 .

[16] C. Weibel,et al. AN INTRODUCTION TO HOMOLOGICAL ALGEBRA , 1996 .

[17] J. Weier. Un théorème d'intersection , 1957 .