Comptes Rendus
Algebra
Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 617-652.

We replace a ring with a small -linear category 𝒞, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of 𝒞. We show that this categorified Chern character is homotopy invariant and is well-behaved with respect to the periodicity operator in cyclic cohomology. For this, we also obtain a description of cocycles and coboundaries in the cyclic cohomology of 𝒞 (and more generally, in the Hopf cyclic cohomology of a Hopf-module category) by means of DG-semicategories equipped with a trace on endomorphism spaces.

Received:
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Accepted:
Published online:
DOI: 10.5802/crmath.429
Classification : 18E05, 47A53, 53C99, 58B34

Mamta Balodi 1; Abhishek Banerjee 1

1 Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mamta Balodi; Abhishek Banerjee. Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 617-652. doi : 10.5802/crmath.429. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.429/

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