3:30 pm, Lecture Hall 6
Residues and Duality — abstract and concrete approaches
Pramathanath Sastry
Chennai Mathematical Institute.
30-09-19

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Abstract

This is a series of talks on concrete and abstract aspects of Grothendieck duality. Grothendieck duality is a vast generalisation of Serre Duality. The original approach of Grothendieck (one which Grothendieck did not like) involved auxiliary constructions like dualizing and residual complexes. A more conceptual approach was initiated by Deligne in 1966, with important additions by Verdier. The problem with the more conceptual approach is the lack of concrete formulas for traces for smooth proper maps and for residues, not even for projective space. Recently Suresh Nayak and the speaker showed that the approach of Deligne and Verdier in fact do give all the residue formulae and nail down traces for smooth proper maps.

The first talk will give the broad picture outlining the two approaches.