Hopf-cyclic homology and cohomology with coefficients

Autor: Hajac, P. M., Khalkhali, M., Rangipour, B., Sommerhaeuser, Y.

Following the idea of an invariant differential complex, we construct general-type cyclic modules that provide the common denominator of known cyclic theories. The cyclicity of these modules is governed by Hopf-algebraic structures. We prove that the

Externí odkaz: http://arxiv.org/abs/math/0306288

Cyclic homology, cdh-cohomology and negative K-theory

Autor: Cortiñas, G., Haesemeyer, C., Schlichting, M., Weibel, C. A.

Publikováno v: Ann. Math. 167, (2008) 549-573

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal $K$-theory satisfies $cdh$-descent. Combining that result with some computations of the $cdh$-cohomology of the sheaf of regular functions, we verify a conjecture

Externí odkaz: http://arxiv.org/abs/math/0502255

Hopf-cyclic homology and cohomology with coefficients

Autor: Bahram Rangipour, Masoud Khalkhali, Yorck Sommerhäuser, Piotr M. Hajac

Publikováno v: Comptes Rendus Mathematique. 338:667-672

Following the idea of an invariant differential complex, we construct general-type cyclic modules that provide the common denominator of known cyclic theories. The cyclicity of these modules is governed by Hopf-algebraic structures. We prove that the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::86232b60f89f1fca4427ce82e1bcae7d
https://doi.org/10.1016/j.crma.2003.11.036

Products and Kunneth theorems in cyclic homology and cohomology theories

Autor: Hood, Christine Elizabeth

This thesis is concerned with the construction of products in cyclic homology and cohomology, by use of the methods of acyclic models. A theory HC ˉ͙ (A) which is dual to cyclic cohomology HC *(A) over its natural coefficients is introduced, and pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=core_ac_uk__::1e4007226fe5cecf576c175b9e30893f
http://wrap.warwick.ac.uk/131937/1/WRAP_Theses_Hood_1985.pdf

The categorified Grothendieck-Riemann-Roch theorem

Autor: Pavel Safronov, Nicolò Sibilla, Marc Hoyois, Sarah Scherotzke

Publikováno v: Hoyois, M, Safronov, P, Scherotzke, S & Sibilla, N 2021, ' The categorified Grothendieck-Riemann-Roch theorem ', Compositio Mathematica, vol. 157, no. 1, pp. 154-214 . https://doi.org/10.1112/S0010437X20007642
Compositio Mathematica

In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for To\"en and Vezzosi's secondary Chern character. As a main application, we establish a compari

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::57c32f66081c7120f218282fd89bf72b
http://hdl.handle.net/20.500.11767/128270