Stratifying triangulated categories (2009)
Benson, Dave, Iyengar, Srikanth B., Krause, Henning
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is...
Homological dimensions and regular rings (2009)
Iacob, Alina, Iyengar, Srikanth B.
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 the problem on hand...
Support and injective resolutions of complexes over commutative rings (2009)
Chen, Xiao-Wu, Iyengar, Srikanth B.
Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. These also give...
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...
On the existence of star products on quotient spaces of linear Hamiltonian torus actions (2008)
Herbig, Hans-Christian, Iyengar, Srikanth B., Pflaum, Markus J.
We discuss BFV deformation quantization of singular symplectic quotient spaces in the special case of linear Hamiltonian torus actions. In particular, we show that the Koszul complex on the moment...
Stratifying modular representations of finite groups (2008)
Benson, Dave, Iyengar, Srikanth B., Krause, Henning
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the...
Linearity defects of modules over commutative rings (2008)
Iyengar, Srikanth B., Roemer, Tim
This paper concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point...
Dimensions of triangulated categories via Koszul objects (2008)
Bergh, Petter Andreas, Iyengar, Srikanth B., Krause, Henning, Oppermann, Steffen
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings....
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)
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...
Local cohomology and support for triangulated categories (2007)
Benson, Dave, Iyengar, Srikanth B., Krause, Henning
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local...
Free resolutions, and depth for complexes (1998)
In Chapter 1, projective resolutions of modules over a ring R are constructed starting from appropriate projective resolutions over a ring Q mapping to R. It is shown that such resolutions may be...