24 citations · 41 across the 21 of their papers we have counts for
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Polynomial growth of Betti sequences over local rings
Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
This is a study of the sequences of Betti numbers of finitely generated modules over a complete intersection local ring, . The subsequences with even,…
Persistence of homology over commutative noetherian rings
Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh +1
We describe new classes of noetherian local rings whose finitely generated modules have the property that for implies that has finite projecti…
Restricting homology to hypersurfaces
Luchezar L. Avramov, Srikanth B. Iyengar
This paper concerns the homological properties of a module over a commutative noetherian ring relative to a presentation , where is local ring. It is proved…
Big Cohen-Macaulay modules, morphisms of perfect complexes, and intersection theorems in local algebra
Luchezar L. Avramov, Srikanth B. Iyengar, Amnon Neeman
There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the…
Homology over trivial extensions of commutative DG algebras
Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh +1
Conditions on the Koszul complex of a noetherian local ring guarantee that is non-zero for infinitely many , when and are finitely genera…
Subadditivity of syzygies of Koszul algebras
Luchezar L. Avramov, Aldo Conca, Srikanth B. Iyengar
Estimates are obtained for the degrees of minimal syzygies of quotient algebras of polynomial rings. For a class that includes Koszul algebra in almost all characteristics, these d…
Bass numbers over local rings via stable cohomology
Luchezar L. Avramov, Srikanth B. Iyengar
For any non-zero finite module M of finite projective dimension over a noetherian local ring R with maximal ideal m and residue field k, it is proved that the natural map Ext_R(k,M…
A cohomological study of local rings of embedding codepth 3
Luchezar L. Avramov
The generating series of the Bass numbers of local rings with residue field are computed in closed rational form, in case the…
Homological invariants of modules over contracting endomorphisms
Luchezar L. Avramov, Melvin Hochster, Srikanth B. Iyengar +1
It is proved that when R is a local ring of positive characteristic, is its Frobenius endomorphism, and some non-zero finite R-module has finite flat dimension or finite inject…
Quasi-complete intersection homomorphisms
Luchezar L. Avramov, Inês B. Henriques, Liana M. Şega
Extending a notion defined for surjective maps by Blanco, Majadas, and Rodicio, we introduce and study a class of homomorphisms of commutative noetherian rings, which strictly cont…
Short Koszul modules
Luchezar L. Avramov, Srikanth B. Iyengar, Liana M. Sega
This article is concerned with graded modules M with linear resolutions over a standard graded algebra R. It is proved that if such an M has Hilbert series of the form $ps…
Cohomology over complete intersections via exterior algebras
Luchezar L. Avramov, Srikanth B. Iyengar
A general method for establishing results over a commutative complete intersection local ring by passing to differential graded modules over a graded exterior algebra is described.…
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…
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…
Gorenstein algebras and Hochschild cohomology
L. L. Avramov, S. Iyengar
For homomorphism K-->S of commutative rings, where K is Gorenstein and S is essentially of finite type and flat as a K-module, the property that all non-trivial fiber rings of K-->…
Homology of perfect complexes
L. L. Avramov, R. -O. Buchweitz, S. B. Iyengar +1
It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result…
Class and rank of differential modules
Luchezar L. Avramov, Ragnar-Olaf Buchweitz, Srikanth Iyengar
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over gr…
Stable cohomology over local rings
Luchezar L. Avramov, Oana Veliche
The focus of this paper is on a poorly understood invariant of a commutative noetherian local ring with residue field : the stable cohomology modules ,…
Gaps in Hochschild cohomology imply smoothness for commutative algebras
Luchezar Avramov, Srikanth Iyengar
The paper concerns Hochschild cohomology of a commutative algebra S, which is essentially of finite type over a commutative noetherian ring K and projective as a K-module, with coe…
Homology over local homomorphisms
Luchezar L. Avramov, Srikanth Iyengar, Claudia Miller
The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorp…
Andre-Quillen homology of algebra retracts
L. L. Avramov, S. Iyengar
Given a homomorphism of commutative noetherian rings , Daniel Quillen conjectured in 1970 that if the Andre-Quillen homology functors vanish for all $n \gg…