**Anandam Banerjee**

TIFR

October 9, 2014

**Equivalence relations on algebraic cobordism**:
Algebraic cobordism gives a lifting of the topological theory of
complex cobordism to the setting of algebraic geometry. As in the case of complex cobordism, algebraic cobordism is closely related to formal group laws, which allows one to construct many new theories from algebraic cobordism. In particular, algebraic $K$-theory and the Chow ring can be obtained in this way. It is an interesting question to ask whether various adequate equivalences for algebraic cycles can be lifted up to the level of algebraic cobordism cycles. After briefly introducing the definition and construction of algebraic cobordism, I will talk about analogues of well-studied equivalence relations at the level of algebraic cobordism cycles and compare them with each other. In particular, I will discuss the behaviour of algebraic cobordism modulo numerical equivalence as a cohomology theory. This work is done jointly with Jinhyun Park.