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Seminar on The Adams spectral sequence and Franke's algebraicity conjecture

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