Yagita’s injectivity conjecture for algebraic cobordism vs. complex cobordism

Establish the injectivity of the natural map from algebraic cobordism to complex cobordism, Ω*(G) -> MU*(K), for every compact connected Lie group K and its complexification G = K_C, thereby resolving Yagita’s conjecture on the relationship between algebraic and topological cobordism of algebraic groups.

Background

The paper recalls the natural comparison map from the algebraic cobordism Ω* of the reductive group G = K_C to the complex cobordism MU* of the corresponding compact connected Lie group K. Yagita conjectured that this map is injective and obtained partial results, but the general case remains unresolved.

The authors focus on Morava K-theory analogues and prove injectivity for specific groups (SO(m) and Spin(m)), but the original cobordism conjecture stays open.