2024/09/05 by Kirill Magidson, Magidson, Kirill
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2409.03877
openalex publication_date 2024/09/05 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28
We give a universal property of the construction of the ring of p-typical Witt vectors of a commutative ring, endowed with Witt vectors Frobenius and Verschiebung, and generalize this construction to the derived setting. We define an ∞-category of p-typical derived δ-Cartier rings and show that the derived ring of p-typical Witt vectors of a derived ring is naturally an object in this ∞-category. Moreover, we show that for any prime p, the formation of the derived ring of p-typical Witt vectors gives an equivalence between the ∞-category of all derived rings and the full subcategory of all derived p-typical δ-Cartier rings consisting of V-complete objects.