Reflexivity and rigidity for complexes. I. Commutative rings (2009)
Avramov, Luchezar L., Iyengar, Srikanth B., Lipman, Joseph
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-rigid complexes....
Reduction of derived Hochschild functors over commutative algebras and schemes (2009)
Avramov, Luchezar L., Iyengar, Srikanth B., Lipman, Joseph, Nayak, Suresh
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 commutative...
Free resolutions over commutative Koszul algebras (2009)
Avramov, Luchezar L., Conca, Aldo, Iyengar, Srikanth B.
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 Koszul and J_1=0 we...
Finite regularity and Koszul algebras (2008)
Luchezar L. Avramov, Irena Peeva
ABSTRACT: We determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite Castelnuovo-Mumford regularity: they are the polynomial...
Luchezar L. Avramov, Vesselin N. Gasharov, Irena V. Peeva
Abstract. A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained...
Free resolutions over short local rings (2008)
Avramov, Luchezar L., Iyengar, Srikanth B., Sega, Liana M.
The structure of minimal free resolutions of finite modules M over commutative local rings (R, 𝔪, k) with 𝔪3 = 0 and rankk(𝔪2)
Frobenius powers of complete intersections (2007)
Luchezar L. Avramov, Claudia Miller
Let R be a commutative noetherian local ring of characteristic p> 0, and let
Luchezar L. Avramov, Daniel R. Grayson
Abstract. The paper contains a new proof and new applications of a theorem of Shamash and Eisenbud, providing a construction of projective resolutions of modules over a complete intersection. The...
Ring Homomorphisms And Finite Gorenstein Dimension (2007)
Luchezar L. Avramov, Hans-Bjørn Foxby
This paper, in which all rings are commutative and noetherian, is devoted to the study of the local structure of ring homomorphisms. Given a ring homomorphism ' : R \Gamma! S, various numerical...
Laurent Coefficients And Ext Of Finite Graded Modules (2007)
Luchezar L. Avramov, Ragnar-Olaf Buchweitz, Judith D. Sally, H Ext I
. Let M and N be finite graded modules over a graded commutative ring generated over a field K = R0 by homogeneous elements x1 ; : : : ; xe of positive degrees d1 ; : : : ; de . By the Hilbert-Serre...
Grothendieck's Localization Problem (2007)
Luchezar L. Avramov, Hans-Bjørn Foxby
. The singularity of a fiber of a flat homomorphism of noetherian rings ' : R ! S at a prime ideal p 2 Spec R is controlled by the singularity of the fiber of ' at any specialization of p...
ANDR E-QUILLEN HOMOLOGY OF ALGEBRA RETRACTS (2007)
Luchezar L. Avramov, Srikanth Iyengar
Let ' : R! S be a homomorphism of commutative noetherian rings. For each n 0, we let Dn (S jR; ) denote the nth cotangent homology functor on the category of S-modules, dened by Andre [1] and...
Finite regularity and Koszul algebras (2007)
Luchezar L. Avramov, Irena Peeva
ABSTRACT: We determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite Castelnuovo-Mumford regularity: they are the polynomial...
Free resolutions over short local rings (2007)
Avramov, Luchezar L., Iyengar, Srikanth B., Sega, Liana M.
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 generic R every M has a...
Constructing modules with prescribed cohomological support (2007)
Avramov, Luchezar L., Iyengar, Srikanth B.
A cohomological support, Supp_A(M), is defined for finitely generated modules M over an left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of...
CLASS AND RANK OF DIFFERENTIAL MODULES (2007)
Buchweitz, Ragnar-Olaf, Avramov, Luchezar L., Iyengar, Srikanth
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 graded rings. We...
Class and rank of differential modules (2006)
Avramov, Luchezar L., Buchweitz, Ragnar-Olaf, Iyengar, Srikanth
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 graded rings. We...
Homology of Perfect Complexes (2006)
Buchweitz, Ragnar-Olaf, Avramov, Luchezar L., Iyengar, Srikanth, Miller, Claudia
http://arXiv.org/abs/math.AC/0609008 v1 31 Aug 2006
Stable cohomology over local rings (2005)
Avramov, Luchezar L., Veliche, Oana
The focus of this paper is on a poorly understood invariant of a commutative noetherian local ring $R$ with residue field $k$: the stable cohomology modules $\hat{Ext}^{n}_R(k,k)$, defined for each...
Buchweitz, Ragnar-Olaf, Avramov, Luchezar L., Sega, Liana M.
Let (R,m, k) be a commutative noetherian local ring with dualizing complex DR, normalized by Extdepth(R) R (k,DR) k. Partly motivated by a long standing conjecture of Tachikawa on (not necessarily...
Homology over local homomorphisms (2003)
Avramov, Luchezar L., Iyengar, Srikanth, Miller, Claudia
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 homomorphism f: R --> S....
The work of Jan-Erik Roos on the cohomology of commutative rings (2002)
This is an attempt to present one aspect of the work of Jan-Erik Roos.
Homotopy Lie algebras and Poincaré series of algebras with monomial relations (2002)
To every homogeneous ideal of a polynomial ring $S$ over a field $K$, Macaulay assigned an ideal generated by monomials in the indeterminates and with the same Hilbert function. Thus, from the point...
Support Varieties and Cohomology over Complete Intersections (2000)
Buchweitz, Ragnar-Olaf, Avramov, Luchezar L.
Archived from publishers website:http:/www/springerlink.metapress.com
Homological Algebra Modulo a Regular Sequence with Special Attention to Codimension Two (2000)
Buchweitz, Ragnar-Olaf, Avramov, Luchezar L.
Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological properties M over R and over Q are intimately...
Luchezar L. Avramov, Srikanth Iyengar
complete intersection homomorphisms
Finite Regularity And Koszul Algebras (2000)
Luchezar L. Avramov, IRENA PEEVA
. We determine the positively graded commutative algebras over which the residue eld modulo the homogeneous maximal ideal has nite Castelnuovo-Mumford regularity: they are the polynomial rings in...
Finite Generation Of Hochschild Homology Algebras (2000)
Luchezar L. Avramov, Srikanth Iyengar
. We prove converses of the Hochschild-Kostant-Rosenberg Theorem, in particular: If a commutative algebra S is at and essentially of nite type over a noetherian ring |, and the Hochschild homology HH...
Support Varieties And Cohomology Over Complete Intersections (2000)
Luchezar L. Avramov, RAGNAR-OLAF BUCHWEITZ
this paper we develop geometric methods for the study of nite modules over a
Classical definitions of locally complete intersection (l.c.i.) homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this...
Resolutions of monomial ideals and cohomology over exterior algebras (1999)
Annetta Aramova, Luchezar L. Avramov, J Urgen Herzog
Abstract. The paper studies the homology of finite modules over the exterior algebra E of a vector space V. To such a module M we associate an algebraic set VE (M) ` V, consisting of those v 2 V that...
Homological Algebra Modulo A Regular Sequence With Special Attention To Codimension Two (1999)
Luchezar L. Avramov, RAGNAR-OLAF BUCHWEITZ
. Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological properties M over R and over Q are intimately...
. Classical definitions of l.c.i. homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this paper is meaningful for...
Evaluating committee: Anders Thorup, University of Copenhagen (1999)
Lars Winther Christensen, Luchezar L. Avramov, Peter Schenzel, Matematisk Afdeling, ...
c ○ Lars Winther Christensen (according to the Danish legislation) ISBN 87-7834-359-3Dear reader, The present manuscript comprises my Ph.D. thesis as submitted to the Faculty of Science at the...
Cohen-Macaulay Properties of Ring Homomorphisms (1998)
Luchezar L. Avramov, Hans-Bjørn Foxby
. Numerical invariants which measure the Cohen--Macaulay character of homomorphisms ' : R ! S of noetherian rings are introduced and studied. Comprehensive results are obtained for homomorphisms...
Complete Intersection Dimension (1997)
Luchezar L. Avramov, Vesselin N. Gasharov, Irena V. Peeva
. A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained for...
Factorial Extensions Of Regular Local Rings And Invariants Of Finite Groups (1996)
Luchezar L. Avramov, Adam Borek
Introduction It is often useful to approach the singularity of a noetherian commutative local domain S from a regular local subring P over which S is finite as a module and residually trivial (that...
Modules With Extremal Resolutions (1996)
Introduction Let R be a commutative noetherian local ring R with maximal ideal m and residue field k = R=m. The size of a minimal free resolution of a finite R--module M is given by its Betti numbers...
Cohomology Operators Defined By A Deformation (1995)
Luchezar L. Avramov, LI-CHUAN SUN
this paper. 2.1. Koszul regularity. Let x = fx 1 ; : : : ; x c g be a set of elements in Q, a = (x) the ideal it generates, and R = Q=a the quotient ring. We denote K the Koszul complex K(x; Q);...
Laurent coefficients and Ext of finite graded modules (1994)
Avramov, Luchezar L., Buchweitz, Ragnar-Olaf, Sally, Judith D.
Let $R=\bigoplus_{n\ges0}R_n$ be a graded commutative ring generated over a field $K=R_0$ by homogeneous elements $x_1,\dots,x_e$ of positive degrees $d_1,\dots,d_e$. The Hilbert-Serre Theorem shows...
Jacobian Criteria For Complete Intersections. The Graded Case (1994)
Luchezar L. Avramov, J Urgen Herzog, Of Kahler Differentials, L. L. Avramov, Jürgen Herzog
. Let P be a positively graded polynomial ring over a field k of characteristic zero, let I be a homogeneous ideal of P , and set R = P=I. The paper investigates the homological properties of some...
Local Rings Over Which All Modules Have Rational Poincaré Series (1994)
. If the homotopy Lie algebra (R) of a local ring R contains a free Lie subalgebra of finite codimension, then for each finitely generated R--modules M the Poncar'e series P R M (t) = P 1 n=0...
Structure of Local Homomorphisms (1994)
Luchezar L. Avramov, Hans-Bjørn Foxby, Bernd Herzog
this paper is to introduce the local stage of a new approach to the study of arbitrary homomorphisms of noetherian rings. If ' : R ! S is a local homomorphism, it involves breaking down the...
Bass Series Of Local Ring Homomorphisms Of Finite Flat Dimension (1993)
Luchezar L. Avramov, Hans-Bjørn Foxby, Jack Lescot
. Nontrivial relations between Bass numbers of local commutative rings are established in case there exists a local homomorphism OE: R ! S which makes S into an R-module of finite flat dimension. In...
Hochschild Homology Criteria For Smoothness (1992)
Luchezar L. Avramov, Micheline Vigué-Poirrier
this paper is to establish a number of converses.
Gorenstein Local Homomorphisms (1990)
Luchezar L. Avramov, Hans-Bjørn FOXBY
Introduction A Noetherian local ring is the algebraic version of a ring of germs of functions defined in neighborhoods of some point of an algebraic (or analytic) variety. Accordingly, local rings...