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20 papers · 1 filter
Homological dimensions and regular rings
Alina Iacob, Srikanth B. Iyengar
A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast th…
Free resolutions over commutative Koszul algebras
Luchezar L. Avramov, Aldo Conca, Srikanth B. Iyengar
For R=Q/J with Q a commutative graded algebra over a field and J non-zero, we relate the slopes of the minimal resolutions of R over Q and of k=R/R_{+} over R. When Q and R are Kos…
Reflexivity and rigidity for complexes. I. Commutative rings
Luchezar L. Avramov, Srikanth B. Iyengar, Joseph Lipman
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rig…
Reduction of derived Hochschild functors over commutative algebras and schemes
Luchezar L. Avramov, Srikanth B. Iyengar, Joseph Lipman +1
We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a…
Constructing Big Indecomposable modules
Andrew Crabbe, Janet Striuli
Let be local Noetherian ring of depth at least two. We prove that there are indecomposable -modules which are free on the punctured spectrum of constant, arbitrarily large,…
Free resolutions over short local rings
Luchezar L. Avramov, Srikanth B. Iyengar, Liana M. Sega
The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)is studied. It is proved that over gene…