ORCID Profile
0000-0001-8789-4438
Current Organisation
University of Tokyo
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Publisher: Societe Mathematique de France
Date: 2017
DOI: 10.24033/BSMF.2739
Publisher: Wiley
Date: 20-05-2021
DOI: 10.1112/S0010437X21007119
Abstract: We prove several results showing that the algebraic $K$ -theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We also give some new proofs of known results concerning cdh descent of algebraic $K$ -theory.
Publisher: Walter de Gruyter GmbH
Date: 2009
DOI: 10.1515/JGT.2008.063
Publisher: Societe Mathematique de France
Date: 2018
DOI: 10.24033/BSMF.2768
Publisher: Springer Science and Business Media LLC
Date: 23-09-2020
Publisher: Springer Science and Business Media LLC
Date: 03-03-2007
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 20-11-2017
DOI: 10.4171/JEMS/754
Publisher: Elsevier BV
Date: 10-2007
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2021
Publisher: Mathematical Sciences Publishers
Date: 12-06-2018
Publisher: Walter de Gruyter GmbH
Date: 14-08-2021
Abstract: We prove that the ∞ {\\infty} -category of motivic spectra satisfies Milnor excision: if A → B {A\\to B} is a morphism of commutative rings sending an ideal I ⊂ A {I\\subset A} isomorphically onto an ideal of B , then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A / I {A/I} that are identified over B / I B {B/IB} . Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub’s étale motives over schemes of finite virtual cohomological dimension.
Publisher: Cambridge University Press (CUP)
Date: 13-09-2019
DOI: 10.1017/NMJ.2019.24
Abstract: In order to work with non-Nagata rings which are Nagata “up-to-completely-decomposed-universal-homeomorphism,” specifically finite rank Hensel valuation rings, we introduce the notions of pseudo-integral closure , pseudo-normalization , and pseudo-Hensel valuation ring . We use this notion to give a shorter and more direct proof that $H_{\\operatorname{cdh}}^{n}(X,F_{\\operatorname{cdh}})=H_{l\\operatorname{dh}}^{n}(X,F_{l\\operatorname{dh}})$ for homotopy sheaves $F$ of modules over the $\\mathbb{Z}_{(l)}$ -linear motivic Eilenberg–Maclane spectrum. This comparison is an alternative to the first half of the author’s volume Astérisque 391 whose main theorem is a cdh-descent result for Voevodsky motives. The motivating new insight is really accepting that Voevodsky’s motivic cohomology (with $\\mathbb{Z}[\\frac{1}{p}]$ -coefficients) is invariant not just for nilpotent thickenings, but for all universal homeomorphisms.
Publisher: Elsevier BV
Date: 10-2015
Publisher: Wiley
Date: 17-07-2014
DOI: 10.1112/S0010437X14007301
Abstract: We show how a theorem of Gabber on alterations can be used to apply the work of Cisinski, Suslin, Voevodsky, and Weibel to prove that $K_n(X) \\otimes \\mathbb{Z}[{1}/{p}]= 0$ for $n {-}\\! \\dim X$ where $X$ is a quasi-excellent noetherian scheme, $p$ is a prime that is nilpotent on $X$ , and $K_n$ is the $K$ -theory of Bass–Thomason–Trobaugh. This gives a partial answer to a question of Weibel.
Publisher: Springer Science and Business Media LLC
Date: 03-04-2019
Publisher: Oxford University Press (OUP)
Date: 29-06-2016
DOI: 10.1093/IMRN/RNW111
Location: France
No related grants have been discovered for Shane Kelly.