• Corpus ID: 238419482

Adams spectral sequences and Franke's algebraicity conjecture

  title={Adams spectral sequences and Franke's algebraicity conjecture},
  author={Irakli Patchkoria and Piotr Pstrkagowski},
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. 

Morava K-theory and Filtrations by Powers

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 $\mathbf C$

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

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. 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

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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

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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

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