Commutative Algebra and Algebraic Geometry: Ring spectra for commutative algebraists

Seminar | January 31 | 2:10-3 p.m. | 939 Evans Hall

 Mengyuan Zhang, UC Berkeley

 Department of Mathematics

We introduce a new category to do commutative algebra in - the stable homotopy category. The talk starts by its construction and properties, with highlights on the comparison with the derived category of abelian groups. We then proceed to examine ring spectra, and generalize (derived) commutative algebra in this new context. Key examples of the talk will be regular ring spectra, gorenstein ring spectra and if time permits complete intersection ring spectra.