| * Venue | Media Centre |
| * Speaker | Sarang Sane |
| * Title | Derived categories supported on certain ideals |
| Affiliation | IIT Madras |
| Abstract | Let A be an abelian category and B be a (full) Serre subcategory in A. It is a classical question as to when the natural functor from the bounded derived category of B to the bounded derived category of A supported on B is an equivalence. When R is a commutative, unital, noetherian ring, A = M (R) is the category of finitely generated R-modules and B is the full subcategory of I-torsion modules for some ideal I of R, the above functor is an equivalence. When R is a finite dimensional regular ring, one can replace M (R) by the full subcategory P (R) of finitely generated projective R-modules. In this talk, we explore what equivalence can be expected when we make this replacement of M (R) by P (R) without any assumption of regularity. We will show how this exploration leads to a characterization of Cohen-Macaulay, local rings, and a similar equivalence as above when I is of finite projective dimension and R has positive characteristic. |
| * Announcement? | Institute |
| * Refreshments? | Before the event |
| * Honorarium? | Faculty |
| Special Arrangements? | None |
| * Host name and email |