Results 1  10
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21
Affine structures and nonarchimedean analytic spaces
"... In this paper we propose a way to construct an analytic space over a nonarchimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of Homological Mirror conjecture and geometric StromingerYauZaslow conjectu ..."
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Cited by 35 (3 self)
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In this paper we propose a way to construct an analytic space over a nonarchimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of Homological Mirror conjecture and geometric StromingerYauZaslow conjecture. In particular, we glue from “flat pieces ” an analytic K3 surface. As a byproduct of our approach we obtain an action of an arithmetic subgroup of the group SO(1,18) by piecewiselinear transformations on the 2dimensional sphere S 2 equipped with naturally defined singular affine structure.
On a Geometric Description of Gal(Q p/Qp) and a padic Avatar of ̂GT
 Duke Math. J
"... We develop a padic version of the socalled GrothendieckTeichmüller theory (which studies Gal ( ¯Q/Q) by means of its action on profinite braid groups or mapping class groups). For every place v of ¯Q, we give some geometricocombinatorial descriptions of the local Galois group Gal ( ¯Qv/Qv) insid ..."
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Cited by 11 (0 self)
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We develop a padic version of the socalled GrothendieckTeichmüller theory (which studies Gal ( ¯Q/Q) by means of its action on profinite braid groups or mapping class groups). For every place v of ¯Q, we give some geometricocombinatorial descriptions of the local Galois group Gal ( ¯Qv/Qv) inside Gal ( ¯Q/Q). We also show that Gal ( ¯Qp/Qp) is the automorphism group of an appropriate π1functor in padic geometry. Contents 1. Introduction..............................
Nonarchimedean tame topology and stably dominated types
 Arxiv.org/pdf/1009.0252 ( janvier 2011
"... Abstract. Let V be a quasiprojective algebraic variety over a nonarchimedean valued field. We introduce topological methods into the model theory of valued fields, define an analogue V of the Berkovich analytification V an of V, and deduce several new results on Berkovich spaces from it. In partic ..."
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Cited by 7 (2 self)
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Abstract. Let V be a quasiprojective algebraic variety over a nonarchimedean valued field. We introduce topological methods into the model theory of valued fields, define an analogue V of the Berkovich analytification V an of V, and deduce several new results on Berkovich spaces from it. In particular we show that V an retracts to a finite simplicial complex and is locally contractible, without any smoothness assumption on V. When V varies in an algebraic family, we show that the homotopy type of V an takes only a finite number of values. The space V is obtained by defining a topology on the prodefinable set of stably dominated types on V. The key result is the construction of a prodefinable strong retraction of V to an ominimal subspace, the skeleton, definably homeomorphic to a space definable over the value group with its piecewise linear structure. 1.
pAdic Analytic Spaces
 DOC. MATH. J. DMV
, 1998
"... This report is a review of results in padic analytic geometry based on a new notion of analytic spaces. I’ll explain the definition of analytic spaces, basic ideas of étale cohomology for them, an application to a conjecture of Deligne on vanishing cycles, the homotopy description of certain analyt ..."
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Cited by 5 (1 self)
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This report is a review of results in padic analytic geometry based on a new notion of analytic spaces. I’ll explain the definition of analytic spaces, basic ideas of étale cohomology for them, an application to a conjecture of Deligne on vanishing cycles, the homotopy description of certain analytic spaces, and a relation between the étale cohomology of an algebraic variety and the topological cohomology of the associated analytic space.
Inseparable local uniformization
"... 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 ..."
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Cited by 4 (0 self)
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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 of valuations and observed that it should
2006): Degenerating families of dendrograms
"... Abstract. A conceptual framework for cluster analysis from the viewpoint of padic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of padic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). Th ..."
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Cited by 3 (3 self)
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Abstract. A conceptual framework for cluster analysis from the viewpoint of padic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of padic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram as a subtree into the BruhatTits tree associated to the padic numbers, and goes back to Cornelissen et al. (2001) in padic geometry. After explaining the definitions, the concept of classifiers is discussed in the context of moduli spaces, and upper bounds for the number of hidden vertices in dendrograms are given. 1.
Riemann Existence Theorems of Mumford Type
, 2008
"... Riemann Existence Theorems for Galois covers of Mumford curves by Mumford curves are stated and proven. As an application, all finite groups are realised as full automorphism groups of Mumford curves in characteristic zero. 1 ..."
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Cited by 3 (2 self)
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Riemann Existence Theorems for Galois covers of Mumford curves by Mumford curves are stated and proven. As an application, all finite groups are realised as full automorphism groups of Mumford curves in characteristic zero. 1
Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology
 J. Algebraic Geom
"... Abstract. We describe the homotopy type of the analytic Milnor fiber in terms of a strictly semistable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser’s motiv ..."
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Cited by 3 (2 self)
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Abstract. We describe the homotopy type of the analytic Milnor fiber in terms of a strictly semistable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser’s motivic Milnor fiber in terms of a strictly semistable model. MSC 2000: 32S30, 32S55, 14D07, 14G22 1.
A nonArchimedean interpretation of the weight zero subspaces of limit mixed Hodge structures
"... ..."
Nonarchimedean geometry of Witt vectors, preprint (2010) available at http://math.mit.edu/~kedlaya/papers
"... Let R be a perfect Fpalgebra, equipped with the trivial norm. Let W (R) be the ring of ptypical Witt vectors over R, equipped with the padic norms. We prove that via the Teichmüller map, the nonarchimedean analytic space (in the sense of Berkovich) associated to R is a (strong) deformation retrac ..."
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Cited by 3 (3 self)
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Let R be a perfect Fpalgebra, equipped with the trivial norm. Let W (R) be the ring of ptypical Witt vectors over R, equipped with the padic norms. We prove that via the Teichmüller map, the nonarchimedean analytic space (in the sense of Berkovich) associated to R is a (strong) deformation retract of the space associated to W (R).