Title: preparation for constructing derived algebraic cobordism
Algebraic cobordism is a generalized cohomology theory for algebraic varieties originally introduced by V. Voevodsky, which is in many ways analogous to complex cobordism in topology. We aim to study a new “elementary” construction of algebraic cobordism, due to T. Annala, which uses derived algebraic geometry and is well-behaved over fields of positive characteristic. In the first talk, I will introduce bivariant theory and some properties of derived algebraic geometry. Next talk I will construct derived algebraic cobordism and compare with Levine-Morel’s algebraic cobordism.