The Gauss–Manin connection on the periodic cyclic homology
A Petrov, D Vaintrob, V Vologodsky - Selecta Mathematica, 2018 - Springer
Let R be the algebra of functions on a smooth affine irreducible curve S over a field k and let
A_ ∙ A∙ be a smooth and proper DG algebra over R. The relative periodic cyclic homology …
A_ ∙ A∙ be a smooth and proper DG algebra over R. The relative periodic cyclic homology …
Non-commutative Cartier operator and Hodge-to-de Rham degeneration
D Kaledin - arXiv preprint math/0511665, 2005 - arxiv.org
We introduce a version of the Cartier isomorphism for de Rham cohomology valid for
associative, not necessarily commutative algebras over a field of positive characteristic …
associative, not necessarily commutative algebras over a field of positive characteristic …
Periodic cyclic homology of certain nuclear algebras
J Brodzki, R Plymen - Comptes Rendus de l'Académie des Sciences-Series …, 1999 - Elsevier
Relying on properties of the inductive tensor product, we construct cyclic type homology
theories for certain nuclear algebras. In this context, we establish continuity theorems. We …
theories for certain nuclear algebras. In this context, we establish continuity theorems. We …
[PDF][PDF] Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology
E Getzler - Israel Math. Conf. Proc, 1993 - Citeseer
It is well-known that the periodic cyclic homology HP•(A) of an algebra A is homotopy
invariant (see Connes [3], Goodwillie [8] and Block [1]). Let A be an algebra over a field k …
invariant (see Connes [3], Goodwillie [8] and Block [1]). Let A be an algebra over a field k …
Motivic structures in non-commutative geometry
D Kaledin - Proceedings of the International Congress of …, 2010 - World Scientific
We review recent theorems and conjectures saying that periodic cyclic homology of a
smooth non-commutative algebraic variety carries all the additional structures the usual de …
smooth non-commutative algebraic variety carries all the additional structures the usual de …
Spectral sequences for cyclic homology
D Kaledin - Algebra, Geometry, and Physics in the 21st Century …, 2017 - Springer
Spectral Sequences for Cyclic Homology Page 1 Progress in Mathematics, Vol. 324, 99–129 c
2017 Springer International Publishing Spectral Sequences for Cyclic Homology D. Kaledin To …
2017 Springer International Publishing Spectral Sequences for Cyclic Homology D. Kaledin To …
[PDF][PDF] On the Gauss-Manin connection in cyclic homology
B Tsygan - arXiv preprint math/0701367, 2007 - arxiv.org
arXiv:math/0701367v1 [math.KT] 13 Jan 2007 Page 1 arXiv:math/0701367v1 [math.KT] 13 Jan
2007 ON THE GAUSS-MANIN CONNECTION IN CYCLIC HOMOLOGY BORIS TSYGAN In …
2007 ON THE GAUSS-MANIN CONNECTION IN CYCLIC HOMOLOGY BORIS TSYGAN In …
Equivariant localization and completion in cyclic homology and derived loop spaces
H Chen - Advances in Mathematics, 2020 - Elsevier
We prove an equivariant localization theorem over an algebraically closed field of
characteristic zero for smooth quotient stacks by reductive groups X/G in the setting of …
characteristic zero for smooth quotient stacks by reductive groups X/G in the setting of …
Non-commutative deformations and quasi-coherent modules
H Dinh Van, L Liu, W Lowen - Selecta Mathematica, 2017 - Springer
We identify a class of quasi-compact semi-separated (qcss) twisted presheaves of algebras
AA for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch …
AA for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch …
Periodic cyclic homology over Q
K Bals - arXiv preprint arXiv:2301.03112, 2023 - arxiv.org
Let $ X $ be a derived scheme over an animated commutative ring of characteristic 0. We
give a complete description of the periodic cyclic homology of $ X $ in terms of the Hodge …
give a complete description of the periodic cyclic homology of $ X $ in terms of the Hodge …