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Creators/Authors contains: "Mathew, Akhil"

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  1. ; ; ; (, Annales Scientifiques de lEcole Normale Supérieure)
    Accepted Manuscript Full Text Available
  2. ; ; ; (, Journal of the American Mathematical Society)
    We prove a purity property in telescopically localized algebraic K-theory of ring spectra: For n ≥ 1, the T (n)-localization of K(R) only depends on the T (0) ⊕ · · · ⊕ T(n)-localization of R. This complements a classical result of Waldhausen in rational K- theory. Combining our result with work of Clausen–Mathew–Naumann–Noel, one finds that LT (n)K(R) in fact only depends on the T (n − 1) ⊕ T (n)-localization of R, again for n ≥ 1. As consequences, we deduce several vanishing results for telescopically localized K-theory, as well as an equivalence between K(R) and TC(τ≥0R) after T (n)-localization for n ≥ 2. 
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  3. (, Tunisian Journal of Mathematics)
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  4. ; (, Forum of Mathematics, Pi)
    Abstract The primary goal of this paper is to identify syntomic complexes with the p -adic étale Tate twists of Geisser–Sato–Schneider on regular p -torsion-free schemes. Our methods apply naturally to a broader class of schemes that we call ‘ F -smooth’. The F -smoothness of regular schemes leads to new results on the absolute prismatic cohomology of regular schemes. 
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  5. ; ; (, Documenta Mathematica)
    We establish various properties of thep-adic algebraic\text{K}-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, thep-adic\text{K}-theory of such rings is homotopy invariant, and coincides with thep-adic\text{K}-theory of thep-adic generic fibre in high degrees. In the case of smooth algebras over perfectoid valuation rings of mixed characteristic the latter isomorphism holds in all degrees and generalises a result of Nizioł. 
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  6. ; ; (, Forum of Mathematics, Sigma)
    Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p , both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate. 
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