Complete Intersections in Rational Homotopy Theory
Shoham Shamir (University of Sheffield)
Monday 18th May, 2009 16:00-17:00 Mathematics Building, room 204
In commutative algebra, complete intersection rings are the "next best thing" after regular rings. The quotient of a polynomial ring by a regular ideal is a prime example of a complete intersection ring. Gulliksen showed that a local Noetherian ring is complete intersection if and only if its homology has polynomial growth. Benson and Greenlees recently characterized local complete intersection rings by a certain structure on their derived categories. These conditions have obvious adaptations into rational homotopy theory. It turns out that, as in commutative algebra, the adapted conditions are also equivalent. I will define the various equivalent conditions, both in commutative algebra and in rational homotopy, and discuss some of the implications of their equivalence. This is joint work with John Greenlees and Kathryn Hess.