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"Ce travail est consacré à la découverte, la définition et l'étude de la courbe fondamentale en théorie de Hodge p-adique. On prend pour cela le point de vue de définir et d'étudier les différents anneaux de périodes p-adiques comme anneaux de fonctions holomorphes de la variable p. L'étude de ces anneaux nous permet de définir la courbe. On classifie ensuite les fibrés vectoriels sur celle-ci, un théorème qui généralise en quelque sortes le théorème de classification des fibrés vectoriels sur la droite projective. Comme application on redémontre géométriquement les deux théorèmes principaux de la théorie de Hodge p-adique : faiblement admissible implique admissible et de Rham implique potentiellement semi-stable"--Back cover.

Hodge theory. --- Curves, Algebraic. --- Vector bundles. --- Arithmetical algebraic geometry --- Théorie de Hodge --- Courbes algébriques --- Fibrés vectoriels --- Géométrie algébrique arithmétique.

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Algebraic geometry --- Number theory --- Hodge theory --- p-adic analysis. --- Théorie de Hodge --- Analyse p-adique --- Hodge theory. --- Variants. --- 51 <082.1> --- Mathematics--Series --- Théorie de Hodge --- p-adic analysis --- Variants --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Complex manifolds --- Differentiable manifolds --- Homology theory --- Analyse p-adique. --- Géométrie algébrique --- Hodge, Théorie de. --- p-adic numbers --- Nombres p-adiques

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The description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), Volume 106, will be forthcoming.

Geometry, Algebraic. --- Hodge theory. --- Torelli theorem. --- Géométrie algébrique --- Théorie de Hodge --- Geometry, Algebraic --- Hodge theory --- Torelli theorem --- 512.7 --- Torelli's theorem --- Curves, Algebraic --- Jacobians --- Complex manifolds --- Differentiable manifolds --- Homology theory --- Algebraic geometry --- Geometry --- Algebraic geometry. Commutative rings and algebras --- 512.7 Algebraic geometry. Commutative rings and algebras --- Géométrie algébrique --- Théorie de Hodge --- Abelian integral. --- Algebraic curve. --- Algebraic cycle. --- Algebraic equation. --- Algebraic geometry. --- Algebraic integer. --- Algebraic structure. --- Algebraic surface. --- Arithmetic genus. --- Arithmetic group. --- Asymptotic analysis. --- Automorphism. --- Base change. --- Bilinear form. --- Bilinear map. --- Cohomology. --- Combinatorics. --- Commutative diagram. --- Compactification (mathematics). --- Complete intersection. --- Complex manifold. --- Complex number. --- Computation. --- Deformation theory. --- Degeneracy (mathematics). --- Differentiable manifold. --- Dimension (vector space). --- Divisor (algebraic geometry). --- Divisor. --- Elliptic curve. --- Elliptic surface. --- Equation. --- Exact sequence. --- Fiber bundle. --- Function (mathematics). --- Fundamental class. --- Geometric genus. --- Geometry. --- Hermitian symmetric space. --- Hodge structure. --- Homology (mathematics). --- Homomorphism. --- Homotopy. --- Hypersurface. --- Intersection form (4-manifold). --- Intersection number. --- Irreducibility (mathematics). --- Isomorphism class. --- Jacobian variety. --- K3 surface. --- Kodaira dimension. --- Kronecker's theorem. --- Kummer surface. --- Kähler manifold. --- Lie algebra bundle. --- Lie algebra. --- Linear algebra. --- Linear algebraic group. --- Line–line intersection. --- Mathematical induction. --- Mathematical proof. --- Mathematics. --- Modular arithmetic. --- Module (mathematics). --- Moduli space. --- Monodromy matrix. --- Monodromy theorem. --- Monodromy. --- Nilpotent orbit. --- Normal function. --- Open set. --- Period mapping. --- Permutation group. --- Phillip Griffiths. --- Point at infinity. --- Pole (complex analysis). --- Polynomial. --- Projective space. --- Pullback (category theory). --- Quadric. --- Regular singular point. --- Resolution of singularities. --- Riemann–Roch theorem for surfaces. --- Scientific notation. --- Set (mathematics). --- Special case. --- Spectral sequence. --- Subgroup. --- Submanifold. --- Surface of general type. --- Surjective function. --- Tangent bundle. --- Theorem. --- Topology. --- Transcendental number. --- Vector space. --- Zariski topology. --- Zariski's main theorem.