Adams Spectral Sequences and Franke’s Algebraicity Conjecture

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.