2025/01/17 by Oisín Flynn-Connolly, Flynn-Connolly, Oisín
Chemistry · Computer Science · Mathematics · #13D03 #18M60 #18M70 #18N40 #Algebraic Topology (math.AT) #Chemical synthesis and alkaloids #FOS: Mathematics #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2501.10164
openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
This is the second in a sequence of three articles exploring the relationship between commutative algebras and E_∞-algebras in characteristic p and mixed characteristic. Given a topological space X, we construct, in a manner analogous to Sullivan's APL-functor, a strictly commutative algebra over \padic which we call the de Rham forms on X. We show this complex computes the singular cohomology ring of X. We prove that it is quasi-isomorphic as an E_∞-algebra to the Berthelot-Ogus-Deligne décalage of the singular cochains complex with respect to the p-adic filtration. We show that one can extract concrete invariants from our model, including Massey products which live in the torsion part of the cohomology. We show that if X is formal then, except at possibly finitely many primes, the p-adic de Rham forms on X are also formal. We conclude by showing that the p-adic de Rham forms provide, in a certain sense, the "best functorial strictly commutative approximation" to the singular cochains complex.