In the reading seminar this term we will go through the paper:

Patchkoria and Pstrągowski, The Adams spectral sequence and Franke's algebraicity conjecture, Arxiv 2110.03669Link opens in a new window, 2021

The authors show that if a stable category is equipped with a homology theory satisfying certain conditions, than it homotopy category is equivalent to the homotopy category of a certain algebraic category of differential objects. This generalizes and proves a conjecture of Franke. In particular this theorem provides sufficient conditions on a ring spectrum for its derived category to be equivalent to the derived category of its homotopy ring, and a proof that the E(n)-local category is algebraic under a certain relation between n and p.

We will meet on Wednesday at 4pm during term 2 in MS.05. Here is an outline of the talks, and a more detailed description of the talks. We thank Irakli Patchkoria for invaluable help in preparing the plan for the seminar.

Please get in touch if you would like to contribute with a talk.

Date	Talk	Speaker	Notes
Jan 12	Overview	Emanuele Dotto
Jan 19	Homology theories and Adams spectral sequences	Emanuele Dotto
Jan 26	The Freyd envelope and epimorphisms	Julie Rasmusen
Feb 2	The prestable Freyd envelope and perfect presheaves	Emanuele Dotto
Feb 9	Prestable enhancements and thread structures	Emanuele Dotto
Feb 16	Bounded and perfect derived categories	Julie Rasmusen
Feb 23	Homology adjunction and the thread structure
Mar 2	Obstruction theory
Mar 9	Proof Part 1: Bousfield adjunction
Mar 16	Proof Part 2: Monadicity