Nonarchimedean Analytic Cyclic Homology

  • Guillermo Cortiñas

    Dep. Matemática-IMAS, FCEyN-UBA, 1428 Buenos Aires, Argentina
  • Ralf Meyer

    Mathematisches Institut, Georg-August Universität Göttingen, Germany
  • Devarshi Mukherjee

    Mathematisches Institut, Georg-August Universität Göttingen, Germany
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Let VV be a complete discrete valuation ring with fraction field FF of characteristic zero and with residue field F\mathbb{F}. We introduce analytic cyclic homology of complete torsion-free bornological algebras over VV. 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 RR is a smooth commutative VV-algebra of relative dimension 11, then we identify the analytic cyclic homology of its dagger completion with Berthelot's rigid cohomology of RVFR\otimes_V\mathbb{F}.

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Guillermo Cortiñas, Ralf Meyer, Devarshi Mukherjee, Nonarchimedean Analytic Cyclic Homology. Doc. Math. 25 (2020), pp. 1353–1419

DOI 10.4171/DM/779