ETALE COHOMOLOGY OF RIGID ANALYTIC VARIETIES AND ADIC SPACES PDF

Show Context Citation Context We generalize theorems of Deligne-Mumford and de Jong on semistable modifications of families of proper curves. The latter can also be characterized by the property that its geometric fibers have no certain exceptional components. The main step of our proof is uniformization of one-dimensional extensions of valued fields. Riemann-Zariski spaces are then used to obtain the result over any integral base.

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Show Context Citation Context We generalize theorems of Deligne-Mumford and de Jong on semistable modifications of families of proper curves. The latter can also be characterized by the property that its geometric fibers have no certain exceptional components. The main step of our proof is uniformization of one-dimensional extensions of valued fields. Riemann-Zariski spaces are then used to obtain the result over any integral base. The defined above Riemann-Zariski spaces are tightly connected to adic spaces of R.

Example 3. Perfectoid spaces by Peter Scholze , " We deduce the weight-monodromy conjecture in certain c For a large class of smooth dagger spaces—rigid spaces with overconvergent structure sheaf—we prove finite dimensionality of de Rham cohomology.

This is enough to obtain finiteness of P. We need a careful study of de Rham cohomology in situati We need a careful study of de Rham cohomology in situations of semistable reduction. Inseparable local uniformization by Michael Temkin " The aim of this paper is to prove that an algebraic variety over a field can be desingularized locally along a valuation after a purely inseparable alteration.

Zariski was first to study the problem of desingularizing algebraic varieties along valuations. He called this problem local uniformization He called this problem local uniformization of valuations and observed that it should by Peter Scholze, Jared Weinstein "

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Etale cohomology of rigid analytic varieties and adic spaces

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Etale Cohomology of Rigid Analytic Varieties and Adic Spaces

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