Semi-topological cobordism for schemes


Jinhyun Park

11:30:00 - 12:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Grothendieck (1958) shows how to define the general notion of the Chern classes for functors satisfying some axioms. It was observed by Quillen that we can obtain more diverse cohomology functors by not requiring the first Chern class map c_1 to be a homomorphism, and this led to the complex cobordism MU^* on the topological category. An analogous step was pursued by Levine and Morel for varieties to define what is called algebraic cobordism. In this talk, we report a recent work that modifies the Levine-Morel cobordism to define a theory that is an algebraic equivalence analogue on cycles. Some known results on non-finite generations of Griffiths groups, etc. are interpreted in terms of this new cobordism theory. This is a joint work with Amalendu Krishna of TIFR.

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