On the structure of CΓ
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چکیده
(ii) (Lazard’s Theorem) L is the polynomial algebra Z[x1, x2, ...]. We proved Lazard’s theorem last semester. We also proved that MU∗ is isomorphic to Z[x1, x2, ...], so MU∗ and L are both polynomial algebras with generators in even degrees (positive even degrees in MU∗, and negative even degrees in L). The usual complex orientation on MU gives rise to a formal group law, and thus we have a homomorphism θ : L→MU∗. Quillen’s Theorem: θ is an isomorphism. In other words, the formal group law associated with MU is the universal one. Given this isomorphism, we can regard MU∗(X) as an L-module.
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تاریخ انتشار 2013