5 papers
Commutative algebra inspired by modularity lifting
Srikanth B. Iyengar
This article gives an overview of some recent results in commutative algebra that are inspired by the work of Wiles, Taylor and Wiles, Diamond, Lenstra and others on the modularity…
The commutative algebra of congruence ideals and applications to number theory
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick…
Unstable elements in cohomology and a question of Lescot
Srikanth B. Iyengar, Sarasij Maitra, Tim Tribone
In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring , Lescot introduces a numerical invariant, denoted , and asks whether…
Homological properties of the module of differentials
Jürgen Herzog, Benjamin Briggs, Srikanth B. Iyengar
These notes were produced by Jürgen Herzog to accompany his lectures in Recife, Brazil, in 1980, on the homological algebra of noetherian local rings. They are are concerned with…
Proxy-small objects present compactly generated categories
Benjamin Briggs, Srikanth B. Iyengar, Greg Stevenson
We develop a correspondence between presentations of compactly generated triangulated categories as localizations of derived categories of ring spectra and proxy-small objects, and…