Geodesic
Nonarchimedean Analytic Cyclic Homology
Documenta mathematica, Tome 25 (2020), pp. 1353-1419
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Let V be a complete discrete valuation ring with fraction field F of characteristic zero and with residue field 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⊗V​F.
DOI : 10.4171/dm/779
Classification : 13D03, 14F30, 14F40, 14G22, 16S88, 19D55
Mots-clés : cyclic homology, bornological algebra, dagger algebra, Leavitt path algebra, excision, Cuntz-Quillen theory 
@article{10_4171_dm_779,
     author = {Devarshi Mukherjee and Guillermo Corti\~nas and Ralf Meyer},
     title = {Nonarchimedean {Analytic} {Cyclic} {Homology}},
     journal = {Documenta mathematica},
     pages = {1353--1419},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/779},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/779/}
}
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Devarshi Mukherjee; Guillermo Cortiñas; Ralf Meyer. Nonarchimedean Analytic Cyclic Homology. Documenta mathematica, Tome 25 (2020), pp. 1353-1419. doi: 10.4171/dm/779

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