Seminar

Oriented cohomology theories provide a general framework to perform intersection-theory style calculations. Prototypical examples include Chow ring, K -theory, and algebraic cobordism, while Annala--Hoyois--Iwasa recently constructed the category MS_S for studying other non-A1-invariant theories. In this talk, we prove a blowup formula for oriented cohomology theories in MS_S. We then give a ring presentation version of this formula and use it to compute oriented cohomology rings of blowups such as the moduli space of complete conics and Mbar_0n. In particular, we demonstrate that one can recover the number 3264 of conics simultaneously tangent to five given ones in P^2 in algebraic cobordism. This is based on joint work with Arkamouli Debnath.