Filtrations and cohomology III: cohomology of E_∞ rings

2025/12/17 by Antieau, Benjamin
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2512.15509

Abstract

We discuss filtrations arising from de Rham-type cohomology theories for E_∞ rings and E_n rings. Examples include the HKR filtration on relative topological Hochschild homology, the Hodge filtration on E_∞ infinitesimal cohomology, and the Hodge filtration on E_∞ de Rham cohomology.

Citations

• Formal Integration of Derived Foliations
• A duality between Lie algebroids and infinitesimal foliations
• Infinitesimal derived foliations
• A motivic filtration on the topological cyclic homology of commutative ring spectra
• Multiplicative structures on Moore spectra
• Perverse schobers and 3d mirror symmetry
• Absolute prismatic cohomology
• E_k-pushouts and E_k+1-tensors
• Coherent cochain complexes and Beilinson t-structures, with an appendix by Achim Krause
• Topological Hochschild homology and Zeta-values
• Hochschild homology and the derived de Rham complex revisited
• The cotangent complex and Thom spectra
• Loday constructions on twisted products and on tori
• Bökstedt periodicity and quotients of DVRs
• Bökstedt periodicity and quotients of DVRs
• Topological Hochschild homology and integral p-adic Hodge theory
• Relative Loday constructions and applications to higher THH-calculations
• Nilpotence and descent in equivariant stable homotopy theory
• Derived Koszul duality and TQ-homology completion of structured ring spectra
• A spectrum-level Hodge filtration on topological Hochschild homology
• A spectral sequence for the homology of a finite algebraic delooping
• An interpretation of E_n-homology as functor homology
• Cohomology theories for highly structured ring spectra
• The McCord model for the tensor product of a space and a commutative ring spectrum

Related

• Filtrations and cohomology I: crystallization
• Filtrations and cohomology II: the Gauss-Manin connection
• Hodge theory and A_∞ structures on cohomology
• q-de Rham cohomology and topological Hochschild homology over ku
• A stacky comparison of the Hodge and Nygaard filtrations