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July 13, 2026Memoirs of the American Mathematical Society3 citationsOpen Access

Adams Spectral Sequences and Franke’s Algebraicity Conjecture

IPIrakli PatchkoriaPPPiotr Pstrągowski

Key Points

  • This work aims to explore the relationship between well-behaved homology theories and the associated derived ∞-categories, particularly in context of Franke's conjecture.
  • Associated a derived ∞-category to homology theories to encode the Adams spectral sequence.
  • Applied theoretical frameworks to investigate Franke's conjecture along with the structure of the Adams filtration.
  • Confirmed Franke's conjecture regarding algebraicity in specific homotopy categories.
  • Established that the Adams filtration exhibits homotopy-coherent monoidality.

Abstract

To any well-behaved homology theory we associate a derived ∞ -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.

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Cite This Study

Patchkoria et al. (2026) studied this question.

synapsesocial.com/papers/6a547f6d475c38bf615a507chttps://doi.org/10.1090/memo/1636
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