# Adams spectral sequences and Franke's algebraicity conjecture

@inproceedings{Patchkoria2021AdamsSS, title={Adams spectral sequences and Franke's algebraicity conjecture}, author={Irakli Patchkoria and Piotr Pstrkagowski}, year={2021} }

To any well-behaved homology theory we associate a derived $\infty$-category which encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on algebraicity of certain homotopy categories and establish homotopy-coherent monoidality of the Adams filtration.

## 6 Citations

### Morava K-theory and Filtrations by Powers

- Mathematics
- 2021

We prove the convergence of the Adams spectral sequence based on Morava Ktheory and relate it to the filtration by powers of the maximal ideal in the Lubin–Tate ring through a Miller square. We use…

### Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf C$

- Mathematics
- 2021

We exhibit a relationship between motivic homotopy theory and spectral algebraic geometry, based on the motivic τ -deformation picture of Gheorghe, Isaksen, Wang, Xu. More precisely, we identify…

### Invertible objects in Franke's comodule categories

- Mathematics
- 2022

. We study the Picard group of Franke’s category of quasi-periodic E 0 E -comodules for E a 2-periodic Landweber exact cohomology theory of height n such as Morava E -theory, showing that for 2 p − 2…

### Dirac geometry I: Commutative algebra

- Mathematics
- 2022

The homotopy groups of a commutative algebra in spectra form a commutative algebra in the symmetric monoidal category of graded abelian groups. The grading and the Koszul sign rule are remnants of…

### Adams-type maps are not stable under composition

- Computer ScienceProceedings of the American Mathematical Society, Series B
- 2022

This work gives a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition, and shows that over a field, this failure is quite extreme, as any map to an algebra is a transfinite composition of Adams- type maps.

### Multiplicative structures on Moore spectra

- Mathematics
- 2022

. In this article we show that S / 8 is an E 1 -algebra, S / 32 is an E 2 -algebra, S /p n +1 is an E n -algebra at odd primes and, more generally, for every h and n there exist generalized Moore…