Sur la p-dimension des corps

Gabber, Ofer; Orgogozo, Fabrice

doi:10.1007/s00222-008-0133-y

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…XVIII].) On the other hand, cd p (K) = 2 was shown by Kato, see [47], or [24] for a more general result. We now use results on Serre's conjecture II: By [28], if H is a semi-simple, simply connected quasi-split reductive group with no E 8 factors, then H 1 (K, H) = ( 1).…”

Section: 22mentioning

confidence: 94%

Integral models of Shimura varieties with parahoric level structure

2018

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For a prime p > 2, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G, X) of abelian type, such that G splits over a tamely ramified extension of Qp. The local structure of these integral models is related to certain "local models", which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on their sheaf of nearby cycles. Bruhat-Tits, a connected smooth group scheme G • over Z p

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Section: 22mentioning

confidence: 94%

Integral models of Shimura varieties with parahoric level structure

2018

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“…By the main result of [GO08] (which is due to [Kat82] in this case), it follows that the Galois group has -cohomological dimension at most . Moreover, by Theorem 4.8, it follows that if is any finite extension of and the ring of integers (which is excellent as a complete local ring), then is -truncated.…”

Section: Pro-galois Descentmentioning

confidence: 93%

“…Working stalkwise on and using the compatibility of étale cohomology with filtered colimits, we can now reduce to the case where is an excellent, strictly henselian normal local domain with residue field (and is contained in the maximal ideal), since excellence and normality are preserved by strict henselization (see [Gre76] for the former). The statement then becomes that for , which follows from the Gabber–Orgogozo bound [GO08, Theorem 6.1] (noting that the -dimension of the residue field is since is separably closed).…”

Section: Asymptotic -Localitymentioning

confidence: 99%

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On -local

Mathew¹

2021

Compositio Math.

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We discuss some general properties of $\mathrm {TR}$ and its $K(1)$ -localization. We prove that after $K(1)$ -localization, $\mathrm {TR}$ of $H\mathbb {Z}$ -algebras is a truncating invariant in the Land–Tamme sense, and deduce $h$ -descent results. We show that for regular rings in mixed characteristic, $\mathrm {TR}$ is asymptotically $K(1)$ -local, extending results of Hesselholt and Madsen. As an application of these methods and recent advances in the theory of cyclotomic spectra, we construct an analog of Thomason's spectral sequence relating $K(1)$ -local $K$ -theory and étale cohomology for $K(1)$ -local $\mathrm {TR}$ .

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“…If is complete, contains a coefficient field [Mat86, Theorem 28.3], and a choice of a system of parameters yields a finite injective map . By Lemma 2.6 it now suffices to show that But in view of Lemma 2.5 this follows from the fact that if form a -basis of , then form a -basis of and of ; see [GO08, Lemma 2.1.5].…”

Section: Preliminaries On the P-dimensionmentioning

confidence: 99%