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Article Dans Une Revue Journal of the American Mathematical Society Année : 2021

K-THEORY AND TOPOLOGICAL CYCLIC HOMOLOGY OF HENSELIAN PAIRS

Résumé

Given a henselian pair (R, I) of commutative rings, we show that the relative K-theory and relative topological cyclic homology with finite coefficients are identified via the cy-clotomic trace K → TC. This yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity theorem (for mod n coefficients, with n invertible in R) and McCarthy's theorem on relative K-theory (when I is nilpotent). We deduce that the cyclotomic trace is an equivalence in large degrees between p-adic K-theory and topological cyclic homology for a large class of p-adic rings. In addition, we show that K-theory with finite coefficients satisfies continuity for complete noetherian rings which are F-finite modulo p. Our main new ingredient is a basic finiteness property of TC with finite coefficients.
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Dates et versions

hal-02385608 , version 1 (28-11-2019)

Identifiants

  • HAL Id : hal-02385608 , version 1

Citer

Dustin Clausen, Akhil Mathew, Matthew Morrow. K-THEORY AND TOPOLOGICAL CYCLIC HOMOLOGY OF HENSELIAN PAIRS. Journal of the American Mathematical Society, 2021, 34, pp.411 - 473. ⟨hal-02385608⟩
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