Last edited by Kazidal
Sunday, August 2, 2020 | History

4 edition of Etale cohomology of rigid analytic varieties and adic spaces found in the catalog.

Etale cohomology of rigid analytic varieties and adic spaces

Roland Huber

# Etale cohomology of rigid analytic varieties and adic spaces

## by Roland Huber

Written in English

Subjects:
• Geometry, Algebraic.,
• Homology theory.,
• Analytic spaces.

• Edition Notes

Includes bibliographical references (p. 443-445) and indexes.

Classifications The Physical Object Statement Roland Huber. Series Aspects of mathematics., v. 30 LC Classifications QA564 .H83 1996 Pagination x, 450 p. ; Number of Pages 450 Open Library OL621528M ISBN 10 3528067942 LC Control Number 96220454 OCLC/WorldCa 36037442

There are some foundational questions on adic spaces that I can't find in the literature. It seems that these questions are pretty natural, so I guess that an answer should be known to the experts in the field. cohomology of such spaces. In addition to constructing higher direct images, we establish their compatibility with base change (Theorem ) and give a relative version of the ´etale-de Rham comparison isomorphism for rigid analytic spaces constructed by Scholze [19] (Theorem ). Note.

(H2) A generalization of formal schemes and rigid-analytic varieties, by Huber (H3) Etale cohomology of rigid-analytic varieties and adic spaces, by Huber (P) Maximally complete fields, by Poonen (S1) Perfectoid spaces, by Scholze (S2) Perfectoid spaces: a survey, by Scholze (S3) p-adic Hodge theory for rigid-analytic varieties, by Scholze. 2In this paper, we work with rigid analytic spaces and their étale cohomology using Huber’s adic spaces [Hub96], but our results could easily be formulated using Berkovich spaces instead. 3(More generally, one can allow any quasiseparated rigid space admitting a covering by countably many quasi-compact open subsets.) 2.

A. J. De Jong, Étale fundamental groups of non-archimedean analytic spaces; Yakov Varshavsky, p-adic uniformization of unitary Shimura varieties; Elena Mantovan, On non-basic Rapoport-Zink spaces; Antoine Ducros, Les espaces de Berkovich sont excellents. Abstract. The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption.

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### Etale cohomology of rigid analytic varieties and adic spaces by Roland Huber Download PDF EPUB FB2

Étale Cohomology of Rigid Analytic Varieties and Adic Spaces (Aspects of Mathematics (30)) Softcover reprint of the original 1st ed. Edition by Roland Huber (Author) › Visit Amazon's Roland Huber Page. Find all the books, read about the author, and more.

See search. First general properties of the étale topos of an adic space are studied, in particular the points and the constructible sheaves of this topos. After this the basic results on the étale cohomology of adic spaces are proved: base change theorems, finiteness, Poincaré duality, comparison theorems with.

The aim of this book is to give an introduction to adic spaces and to develop systematically their étale cohomology. First general properties of the étale topos of an adic space are studied, in particular the points and the constructible sheaves of this topos.

After this the basic results on the. Etale cohomology of rigid analytic varieties and adic spaces. Braunschweig: Vieweg, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Roland Huber.

Etale Cohomology of Rigid Analytic Varieties and Adic Spaces. Front Cover Adic spaces. The etale site of a rigid analytic variety and an adic space. Results 1 – 10 of 10 Etale Cohomology of Rigid Analytic Varieties and Adic Spaces by Roland Huber and a great selection of related books, art and collectibles.

Étale cohomology of rigid analytic varieties and adic spaces. By Roland Huber. Cite. The aim of this book is to give an introduction to adic spaces and to develop systematically their étale cohomology. First general properties of the étale topos of an adic space are studied, in particular the points and the constructible sheaves of.

In this chapter we summarize our results on the étale cohomology of rigid analytic varieties which will be proved more generally for adic spaces in later chapters.

Our general reference for rigid analytic varieties is [BGR], [FP].Author: Roland Huber. Huber, R., Étale Cohomology of Rigid Analytic Varieties and Adic Spaces, Aspects of Mathematics, E30 (Friedr. Vieweg & Sohn, Braunschweig, ).

de Jong, A. J., ‘ Étale fundamental groups of non-Archimedean analytic spaces ’, Compositio Math. 97 (1–2) (), 89 –special issue in honour of Frans Oort.

analytic spaces. Several di culties have to be overcome to make this work. The rst is that niteness of p-adic etale cohomology is not known for rigid-analytic varieties over p-adic elds. In fact, it is false if one does not make a restriction to the proper case. However, our. purity theorem, and an application of perfectoid spaces to the etale cohomology of smooth proper analytic spaces.

Reference (for nal two meetings): (S3) Scholze, p-adic Hodge theory for rigid-analytic varieties, Forum of Math. (), 1{ Lecture 22 (April 8, Masullo): Deformation theory of. [Hu] R Huber, Étale cohomology of rigid analytic varieties and adic spaces, Preprint, July MR [dJ] A.J.

de Jong, Crystalline Dieudonné module theory via formal and rigid geometry, to appear. Zbl [JP] A.J. de Jong and M. van der Put, Étale cohomology of rigid analytic spaces, Preprint of the University of Groningen. References.

Backgroud material on adic and perfectoid spaces; Arizona Winter School Perfectoid Spaces.; Peter Scholze, Jared Weinstein, Lectures on p-adic geometry.

Peter Scholze, Perfectoid spaces. Bhargav Bhatt, Peter Scholze, The pro-etale topology for schemes. Roland Huber, Etale Cohomology of Rigid Analytic Varieties and Adic Spaces.

Following an old suggestion of Clozel, recently realized by Harris-Lan-Taylor-Thorne for characteristic $0$ cohomology classes, one realizes the cohomology of the locally symmetric spaces for $\mathrm{GL}_n$ as a boundary contribution of the cohomology of symplectic or unitary Shimura varieties, so that the key problem is to understand torsion.

Gabber and Ramero's book on Almost ring theory; Huber's Continuous valuations and A generalization of formal schemes and rigid analytic varieties; Huber's book Etale cohomology of rigid analytic varieties and adic spaces (available through UM) Wedhorn's notes on adic spaces.

logarithmic de rham comparison for open rigid spaces - volume 7 - shizhang li, xuanyu pan. Get this from a library. Etale cohomology of rigid analytic varieties and adic spaces. [Roland Huber]. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology.

Idea. Rigid analytic geometry (often just “rigid geometry” for short) is a form of analytic geometry over a nonarchimedean field K K which considers spaces glued from polydiscs, hence from maximal spectra of Tate algebras (quotients of a K K-algebra of converging power series).This is in contrast to some modern approaches to non-Archimedean analytic geometry such as Berkovich spaces which.

For p-adic realizations, a natural approach would consist in associating to a variety (more generally, a motive) over k a rigid analytic “variety” (better saying, a rigid analytic motive) over complete valued field K of characteristic 0 and residue equal to.

We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of. Roland Huber is the author of Etale Cohomology Of Rigid Analytic Varieties And Adic Spaces ( avg rating, 1 rating, 1 review, published )5/5.Abelian varieties.- Points of rigid spaces, rigid cohomology.- Etale cohomology of rigid spaces.- Covers of algebraic curves.- Etale Cohomology of Rigid Analytic Varieties and Adic Spaces.

Book.In this paper, we study local constancy of ´etale cohomology of rigid analytic varieties over K, or more precisely, of adic spaces of ﬁnite type over Spa(K,O).

A main result. The theory of ´etale cohomology for adic spaces was developed by Huber; see [11]. Huber obtained several ﬁniteness results on ´etale cohomology of adic.