This is the class webpage for my topics class at Harvard (Spring ’20). The goal is to give an overview of Levine-Morel’s algebraic cobordism via various perspectives.
- Lecture 1: antecedents and overview (last updated January 31)
- Lecture 2: derived commutative rings (last updated Feb 5; exercises modified)
- lecture 3: derived schemes (last updated Feb 6)
- lecture 4: Chow homology and oriented Borel-Moore functors (last updated Feb 6; with appendix)
- lectures 5+6: Koszul derived subschemes, the Hurewicz theorem, quasi-smoothness and classification of derived structures (last updated Feb 15) (thanks to Xu Kai for pointing out an earlier gap in the proof of 0.0.2)
- Lecture 7: the definition of algebraic cobordism
- Guest lecture by Martin Speirs.
- Lecture 8: derived double points
- Lecture 9: derived blow-ups and formal group laws
- Lecture 10: Lazard’s theorem and Quillens theorem, constructing an FGL I
- Lecture 11: constructing an FGL II, derived double point relations
A reading list:
- Derived algebraic geometry by Bertrand Toën
- Jacob Lurie’s thesis
- SGA 6
Fabien Morel
Marc Levine; PC: M. Yakerson
PC: MFO
Elden Elmanto 