Pro-etale topology for schemes
Webb11 apr. 2024 · A key role in the proof is played by a comparison between cohomology groups of an admissible Zariski-Riemann space with respect to different topologies; namely, the rh-topology which is related to K-theory as well as the Zariski topology whereon the cohomology groups in question rely. 1 Introduction Webb3.The pro-étale fundamental group Let X be a locally noetherian scheme. Theorem 3.1 ([2], 7.3.9). For a sheaf Fon Xpro-et, the following are equivalent: IFis locally constant, i.e. …
Pro-etale topology for schemes
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WebbThis article continues the study started in [], where we dealt with the Künneth formula, general van Kampen theorem and the comparison between “geometric” and “arithmetic” fundamental groups in the case of $\pi _1^{{\mathrm{pro}}\acute{\mathrm{e}}{\mathrm{t}}}$ .The main result, however, does … WebbSection 59.4 (03N4): The étale topology—The Stacks project 59.4 The étale topology It is very hard to simply “add” extra open sets to refine the Zariski topology. One efficient way to define a topology is to consider not only open sets, but …
Webbattached to any scheme which has similar applications as for ordinary topological spaces. This leads to the notion of the étale homotopy type. The starting observation is the … WebbTHE PRO-ETALE TOPOLOGY FOR SCHEMES´ by Bhargav Bhatt & Peter Scholze To Ge´rard Laumon, with respect and admiration Abstract.—We give a new definition of the derived …
WebbIn algebraic geometry, the étale topologyis a Grothendieck topologyon the category of schemeswhich has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic. Webb31 dec. 2014 · To accomplish these tasks, we define and study the pro-etale topology, which is a Grothendieck topology on schemes that is closely related to the etale …
Webbcontractibility of the pro-´etale topology and pro-( etale) versus pro-´ ´etale, associating the sheaf in the pro-etale topology to a pro-finite space, and, lastly, the infinite Galois …
WebbTHE PRO-ETALE TOPOLOGY FOR ALGEBRAIC STACKS CHANG-YEON CHOUGH Abstract. The pro- etale topology by Bhargav Bhatt and Peter Scholze allows us to recon-struct … nz tenancy inspectionWebb1 maj 2004 · Abstract. We compare Friedlander's definition of the étale topological type for simplicial schemes to another definition involving realizations of pro-simplicial sets. This … nzte international business awardsWebb(Pro)Etale Cohomology Lecture 12. Topology II In this talk we de ne the pro- etale site of a scheme, giving a number of examples of pro- etale schemes. We discuss the case of a … nzte leadership teamWebb11 apr. 2024 · We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely … maharashtra bed cet entrance exam 2022Webb4 sep. 2013 · In [Bhatt-Scholze, The Pro-\'etale Topology for Schemes], B. Bhatt and P. Scholze introduced the notion of the pro-\'etale fundamental group for a connected … maharashtra bed entrance examWebbLet X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this work we define a complex Kn,X,log via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves ν̃n,X to Kn,X,log for the étale … nz term times 2023Webbpro et have pro nite underlying topological space (i.e., compact, Hausdor , totally disconnected topological space), it follows that any qcqs Xalso has pro nite underlying … maharashtra bed cet form 2023