Last modified date: <%+ tp.file.last_modified_date() %>
 Tags:
 Refs:
 Links:
Formal Groups and Spectra
Formal Groups
Basics

Motivation: why should one care about formal groups?
 Idea: substitute for Lie algebras in positive characteristic
 Formal group and lie algebra carry the same info in char 0
 Functor: LieGroups (or AlgGrp) → LieAlgebras factors through FormalGroups

Motivation: if a formal group were for sale, why might you buy it?
 What is a formal group law?
 Why is the group law called “formal”?
 How “should” one think of a formal group?
 What is a formal exponential and formal logarithm?
 What are examples of formal groups? What is a morphism? When are they isomorphic?
 What are the additive and multiplicative formal groups?
 How are the additive and multiplicative formal groups related?
 What is the height of a formal group?
 How can one extend formal groups over rings R to algebras over R?
 What is the formal scheme interpretation of formal groups?
 How does iterated Ktheory show up in the theory of formal groups?
Other Connections to Elliptic Curves
 What is the invariant differential of an elliptic curve?
 How does one extract the formal group of an elliptic curve using differential forms?
 How does the formal group of a curve relate to torsion and the MordellWeil theorem?
 How do formal groups arise from Projects/2022 Advanced Qual Projects/Elliptic Curves/Elliptic Curves?
 What can a formal group tell you about your curve?
Lazard Ring
 What is the Lazard ring?
 What does it mean to be a “universal” coefficient ring?
 How exactly is the Lazard ring universal?

How are formal groups related to spectra?

What is MU?

How are formal groups related to cobordism?
 What is a complex oriented cohomology theory?
 How is the Lazard ring directly related to cobordism classification?
 What is the moduli stack of formal groups?
Stable Homotopy
tmf
 How is tmf related to modular forms?
 How is tmf defined in terms of the moduli stack of elliptic curves?
KTheories
 How is the algebraic Ktheory of a commutative ring defined/constructed in terms of monoidal categories?