Geodesic
Nonarchimedean Analytic Cyclic Homology
Documenta mathematica, Tome 25 (2020), pp. 1353-1419.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $V$ be a complete discrete valuation ring with fraction field $F$ of characteristic zero and with residue field $\mathbb{F}$. We introduce analytic cyclic homology of complete torsion-free bornological algebras over $V$. We prove that it is homotopy invariant, stable, invariant under certain nilpotent extensions, and satisfies excision. We use these properties to compute it for tensor products with dagger completions of Leavitt path algebras. If $R$ is a smooth commutative $V$-algebra of relative dimension $1$, then we identify the analytic cyclic homology of its dagger completion with Berthelot's rigid cohomology of $R\otimes_V\mathbb{F}$.
Classification : 19D55, 14F30, 14F40, 14G22, 13D03, 16S88
Keywords: cyclic homology, dagger algebra, bornological algebra, Leavitt path algebra, excision, Cuntz-Quillen theory 
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     author = {Corti\~nas, Guillermo and Meyer, Ralf and Mukherjee, Devarshi},
     title = {Nonarchimedean {Analytic} {Cyclic} {Homology}},
     journal = {Documenta mathematica},
     pages = {1353--1419},
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     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a28/}
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Cortiñas, Guillermo; Meyer, Ralf; Mukherjee, Devarshi. Nonarchimedean Analytic Cyclic Homology. Documenta mathematica, Tome 25 (2020), pp. 1353-1419. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a28/