Results 1  10
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120
The Picard scheme
, 2005
"... We develop in detail most of the theory of the Picard scheme that Grothendieck sketched in two Bourbaki talks and in commentaries on them. Also, we review in brief much of the rest of the theory developed by Grothendieck and by others. But we begin with a historical introduction. ..."
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Cited by 73 (3 self)
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We develop in detail most of the theory of the Picard scheme that Grothendieck sketched in two Bourbaki talks and in commentaries on them. Also, we review in brief much of the rest of the theory developed by Grothendieck and by others. But we begin with a historical introduction.
The inverse Galois problem and rational points on moduli spaces
 Math. Annalen
, 1991
"... Abstract: We reduce the regular version of the Inverse Galois Problem for any finite group G to finding one rational point on an infinite sequence of algebraic varieties. As a consequence, any finite group G is the Galois group of an extension L/P(x) with L regular over any PAC field P of characteri ..."
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Cited by 57 (25 self)
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Abstract: We reduce the regular version of the Inverse Galois Problem for any finite group G to finding one rational point on an infinite sequence of algebraic varieties. As a consequence, any finite group G is the Galois group of an extension L/P(x) with L regular over any PAC field P of characteristic zero. A special case of this implies that G is a Galois group over Fp(x) for almost all primes p. Many attempts have been made to realize finite groups as Galois groups of extensions of Q(x) that are regular over Q (see the end of this introduction for definitions). We call this the “regular inverse Galois problem. ” We show that to each finite group G with trivial center and integer r ≥ 3 there is canonically associated an algebraic variety, Hin r (G), defined over Q (usually reducible) satisfying the following.
Noncommutative geometry, quantum fields and motives
 Colloquium Publications, Vol.55, American Mathematical Society
, 2008
"... ..."
Homotopical Algebraic Geometry I: Topos theory
, 2002
"... This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher topos. For this, we use Scategories (i.e. simplicially enriched categories) as models for certain kind of ..."
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Cited by 32 (20 self)
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This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher topos. For this, we use Scategories (i.e. simplicially enriched categories) as models for certain kind of ∞categories, and we develop the notions of Stopologies, Ssites and stacks over them. We prove in particular, that for an Scategory T endowed with an Stopology, there exists a model
Log smooth deformation theory
 Tohoku Math. J
, 1996
"... This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for example, the following two types of deformations: (1) relative def ..."
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Cited by 25 (4 self)
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This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for example, the following two types of deformations: (1) relative deformations of a certain kind of a pair of an algebraic variety and a divisor of it, and (2) global smoothings of normal crossing varieties. The former is a generalization of the relative deformation theory introduced by Makio, and the latter coincides with the logarithmic deformation theory introduced by Kawamata and Namikawa. 1
Finiteness theorems in geometric classfield theory, Enseign
 Math
, 1981
"... Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nichtkommerzielle Zwecke in Lehre, Forschung und für die private Nutzung frei zur Verfügung. Einzelne Dateien oder Ausdrucke aus diesem Angebot können zusammen mit diesen ..."
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Cited by 21 (3 self)
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Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nichtkommerzielle Zwecke in Lehre, Forschung und für die private Nutzung frei zur Verfügung. Einzelne Dateien oder Ausdrucke aus diesem Angebot können zusammen mit diesen Nutzungsbedingungen und unter deren Einhaltung weitergegeben werden.
Irreducible components of rigid spaces
, 1998
"... This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field k. We prove the excellence of the local rings on rigid spaces over k. This is used to prove the standard existence theorems and to show compatibility with the notion of irre ..."
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Cited by 21 (2 self)
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This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field k. We prove the excellence of the local rings on rigid spaces over k. This is used to prove the standard existence theorems and to show compatibility with the notion of irreducible components for schemes and formal schemes. Behavior with respect to extension of the base field is also studied. It is often necessary to augment schemetheoretic techniques with other algebraic and geometric arguments. COMPONANTES IRRÉDUCTIBLE D’ESPACES RIGIDES Cet article donne les fondements de la théorie globale des composantes irréductibles d’espaces analytiques rigides sur un corps complet k. Nous prouvons l’excellence d’anneaux locaux sur les espaces rigides sur k. De là, nous prouvons les théorèmes standards d’existence et nous montrons la compatibilité avec les notions des composantes irréductibles pour les schémas et les schémas formels. Le comportement par rapport à l’extension de corps base est aussi étudié. Il est souvent nécessaire de compléter les techniques de théorie des schémas par d’autres arguments algébriques et géométriques.
Semistable reduction for overconvergent Fisocrystals on a curve
"... We introduce a valuationtheoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the RiemannZariski space associated to the function fiel ..."
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Cited by 20 (14 self)
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We introduce a valuationtheoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the RiemannZariski space associated to the function field of a variety. Contents
Families of wildly ramified covers of curves
 Amer. J. Math
, 2001
"... In this paper, I investigate wildly ramified GGalois covers of curves φ: Y → P 1 k branched at exactly one point over an algebraically closed field k of characteristic p. I answer a question of M. Raynaud by showing that proper families of such covers of a twisted projective line are isotrivial. Th ..."
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Cited by 18 (9 self)
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In this paper, I investigate wildly ramified GGalois covers of curves φ: Y → P 1 k branched at exactly one point over an algebraically closed field k of characteristic p. I answer a question of M. Raynaud by showing that proper families of such covers of a twisted projective line are isotrivial. The method is to construct an affine moduli space for covers whose inertia group is of the form I = Z/p ⋊ µm. There are two other applications of this space in the case that I = Z/p ⋊ µm. The first uses formal patching to compute the dimension of the space of nonisotrivial deformations of φ in terms of the lower jump of the filtration of higher inertia groups. The second gives necessary criteria for good reduction of families of such covers. These results will be used in a future paper to prove the existence of such covers φ with specified ramification data. 1