Formal Integration of Derived Foliations, joint with L.Brantner and J.Nuiten. PDF. Description: In this paper, we develop derived deformation theory in any characteristic, and prove the equivalence between partition Lie algebroids on a given locally cohered scheme and formal moduli problems under that scheme.
Witt Vectors and δ-Cartier Rings. PDF. Description: I develop the theory of Witt vectors of derived rings, show how to package the algebraic structures on Witt vectors (lift of Frobenius and Verschiebung) in terms of the notion of a δ-Cartier rings, and establish a universal property of the ring of Witt vectors of a derived ring as a derived δ-Cartier ring.
Divided Powers and Derived De Rham Cohomology. PDF. Description: I establish a universal property of the Hodge-filtered derived De Rham cohomolgy as a universal filtered derived divided power algebra, and connect this to the classical approach.
Spectral Algebras and Non-commutative Hodge-De Rham Degeneration, joint with D.Kaledin and A.Konovalov. PDF. Description: We prove the non-commutative Hodge-De Rham degeneration conjecture for periodic cyclic homology of a smooth proper dg algebra A in characteristic 0 by lifting A to a spectral algebra and using the Tate valued Frobenius for topological Hochshild homology.
Work in Progress
Differential Graded Cartier Modules and De Rham-Witt complex, in preparation.
Derived Symmetric Monoidal Categories, in preparation with Artem Prikhodko.
Kirill Magidson 