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Percevoir ce qu’était l’espace sacré au Moyen Âge est à la fois simple et complexe, car si la société médiévale est profondément christianisée, il n’en demeure pas moins que déterminer l’espace sacré dans sa dimension spatiale n’est guère aisé. Le lieu sacré est lié à la pratique du culte qui se traduit par des rites et des choix liturgiques. La dimension ecclésiale et collective implique un partage physique et spirituel de cet espace entre d’une part les fidèles, les clercs et les moines et d’autre part les vivants et les morts. Cette partition génère une organisation spatiale perceptible à travers les études architecturales, les aménagements liturgiques et les circulations, mais aussi grâce à la diversité ou la permanence des programmes iconographiques. Le terme d’espace ecclésial ne se rapportant pas uniquement à l’église, il a été jugé nécessaire de s’intéresser également aux lieux qui lui sont associés, comme le cloître et le cimetière. C’est ainsi qu’à travers un grand nombre d’exemples puisés dans les régions Rhône-Alpes et Auvergne, des archéologues, historiens de l’art et liturgistes, issus des diverses institutions de recherche françaises et réunis en « Action collective de recherche », offrent ici une approche croisée de l’espace sacré depuis l’Antiquité tardive jusqu’au xve siècle. L’ouvrage s’appuie sur des études régionales dont plusieurs sont inédites.

Religious architecture --- Architecture, Medieval --- Middle Ages --- Spiritual architecture --- Architecture --- espace sacré --- chapelle --- chœur --- basilique --- nef --- relique --- sanctuaire --- crypte --- transept --- pontifical --- chevet --- ecclesia --- porche --- lithurgie

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Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.

p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Abelian category. --- Acting in. --- Addition. --- Aisle. --- Algebraic closure. --- Algebraic curve. --- Algebraic structure. --- Algebraic variety. --- Allegory (category theory). --- Analytic function. --- Analytic geometry. --- Analytic space. --- Archimedean property. --- Arithmetic. --- Banach algebra. --- Bertolt Brecht. --- Buttress. --- Centrality. --- Clerestory. --- Commutative diagram. --- Commutative property. --- Complex analysis. --- Contradiction. --- Corollary. --- Cosmetics. --- De Rham cohomology. --- Determinant. --- Diameter. --- Differential form. --- Dimension (vector space). --- Divisor. --- Elaboration. --- Embellishment. --- Equanimity. --- Equivalence class (music). --- Existential quantification. --- Facet (geometry). --- Femininity. --- Finite morphism. --- Formal scheme. --- Fred Astaire. --- Functor. --- Gavel. --- Generic point. --- Geometry. --- Gothic architecture. --- Homomorphism. --- Hypothesis. --- Imagery. --- Injective function. --- Irreducible component. --- Iterated integral. --- Linear combination. --- Logarithm. --- Marni Nixon. --- Masculinity. --- Mathematical induction. --- Mathematics. --- Mestizo. --- Metaphor. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Neuroticism. --- Noetherian. --- Notation. --- One-form. --- Open set. --- P-adic Hodge theory. --- P-adic number. --- Parallel transport. --- Patrick Swayze. --- Phrenology. --- Politics. --- Polynomial. --- Prediction. --- Proportion (architecture). --- Pullback. --- Purely inseparable extension. --- Reims. --- Requirement. --- Residue field. --- Rhomboid. --- Roland Barthes. --- Satire. --- Self-sufficiency. --- Separable extension. --- Sheaf (mathematics). --- Shuffle algebra. --- Subgroup. --- Suggestion. --- Technology. --- Tensor product. --- Theorem. --- Transept. --- Triforium. --- Tubular neighborhood. --- Underpinning. --- Writing. --- Zariski topology.