4 papers
Complexity and curvature of pairs of Burch modules and ideals
Souvik Dey, Dipankar Ghosh, Mouma Samanta
The complexity and curvature of a module were first introduced by Avramov to distinguish modules of infinite homological dimension. Later, Avramov-Buchweitz extended the notion of…
Auslander-Reiten conjecture for modules whose (self) dual has finite complete intersection dimension
Dipankar Ghosh, Mouma Samanta
Over a commutative Noetherian ring, we show that the Auslander-Reiten conjecture holds true for the class of (finitely generated) modules whose dual has finite complete intersectio…
Test properties of some Cohen-Macaulay modules and criteria for local rings via finite vanishing of Ext or Tor
Souvik Dey, Dipankar Ghosh, Aniruddha Saha
In this article, we show test properties, in the sense of finitely many vanishing of Ext or Tor, of CM (Cohen-Macaulay) modules whose multiplicity and number of generators (resp.,…
Complexity and curvature of (pairs of) Cohen-Macaulay modules, and their applications
Souvik Dey, Dipankar Ghosh, Aniruddha Saha
The complexity and curvature of a module, introduced by Avramov, measure the growth of Betti and Bass numbers of a module, and distinguish the modules of infinite homological dimen…