We replace a ring with a small -linear category , 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 . 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 (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.
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Mamta Balodi 1; Abhishek Banerjee 1
@article{CRMATH_2023__361_G3_617_0, author = {Mamta Balodi and Abhishek Banerjee}, title = {Fredholm modules over categories, {Connes} periodicity and classes in cyclic cohomology}, journal = {Comptes Rendus. Math\'ematique}, pages = {617--652}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.429}, language = {en}, }
TY - JOUR AU - Mamta Balodi AU - Abhishek Banerjee TI - Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology JO - Comptes Rendus. Mathématique PY - 2023 SP - 617 EP - 652 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.429 LA - en ID - CRMATH_2023__361_G3_617_0 ER -
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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