Vanishing and comparison theorems in rigid analytic geometry. First general properties of the tale topos of an adic space are studied, in. First general properties of the etale topos of an adic space are studied, in particular the points and the constructible sheaves of this topos. Find all the books, read about the author, and more.
In proceedings of the international congress of mathematicians, vol. This is analogous to the notion of manifolds being coverable by open subsets isomorphic to euclidean space, or schemes being coverable by affines. We construct a functor from the category of p adic etale local systems on a smooth rigid analytic variety x over a p adic field to the category of vector bundles with an integrable connection over. Results 1 10 of 10 etale cohomology of rigid analytic varieties and adic spaces by roland huber and a. A rigid analytic space over k is a pair, describing a locally ringed gtopologized space with a sheaf of kalgebras, such that there is a covering by open subspaces isomorphic to affinoids.
Constructibility and reflexivity in nonarchimedean geometry. We nish with some speculations on how a theory that combines all primes p, including the archimedean prime, might look. Syntomic complexes and padic nearby cycles request pdf. Our general reference for rigid analytic varieties. First, there was the fascinating design of a new analytic theory which, for the. Partially proper sites of rigid analytic varieties and.
In section 2 we will note some properties of this cohomology. Finiteness of cohomology of local systems on rigid. This talks gives analogs of classical theorems for curves, like riemanns existence. Number theory learning seminar stanford university. First general properties of the etale topos of an adic space are studied. On torsion in the cohomology of locally symmetric varieties. In the third paragraph we will compare the hausdorff strictly analytic spaces defined by berkovich in ber l with rigid analytic varieties.
The aim of this book is to give an introduction to adic spaces and to develop systematically their etale cohomology. Along the way, we show that branched covers of normal rigid spaces can often be extended across closed analytic subsets, in analogy with a classical result for complex analytic spaces. Rigid cohomology does seem to be a universal p adic cohomology with. Cuspidal representations in the adic cohomology of the rapoportzink space for, preprint, arxiv. The etale site of a rigid analytic variety and an adic space. Diophantine problems and padic period mappings after. Technically, our results rest on our theory of perfectoid spaces, which gives a. This first set of constraints is worked out in the theory of overconvergent global analytic. Etale cohomology for nonarchimedean analytic spaces numdam. S3 scholze, p adic hodge theory for rigid analytic varieties, forum of math. An overview when they were distributed, tates fundamental notes on rigid analytic spaces t immediately received strong attention for several reasons. Several di culties have to be overcome to make this work. Etale cohomology of rigid analytic varieties and adic spaces. 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.
Receiv octob er 16, 1995 unicated comm y b eter p hneider sc ct. Etale cohomology for nonarchimedean analytic spaces weizmann. After this the basic results on the etale cohomology of adic spaces are proved. Using a natural functor from analytic adic spaces over z pto diamonds which identi es etale sites, this induces a similar formalism. Huber constructed an etale cohomology theory for his adic. One important aspect of their argument then is the interplay between the p adic period map and the complex period map.
In fact, it is false if one does not make a restriction to the proper case. 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. Roland huber the aim of this book is to give an introduction to adic spaces and to develop systematically their tale cohomology. The rst is that niteness of p adic etale cohomology is not known for rigid analytic varieties over p adic elds. Available formats pdf please select a format to send.
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