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Philosophy of science --- Induction (Mathematics) --- Mathematical statistics --- Probabilities --- 51 <09> --- Mathematical induction --- Induction (Logic) --- Mathematics --- History --- Mathematics--Geschiedenis van .. --- History. --- Probabilités --- Induction (Mathématiques) --- Statistique mathématique --- Histoire --- Mathematics--Geschiedenis van . --- Mathematics--Geschiedenis van --- Probabilities - History --- Induction (Mathematics) - History --- Mathematical statistics - History

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The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higher-dimensional complex manifolds, modeled on the theory as developed for Riemann surfaces.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Analytical spaces --- Differential geometry. Global analysis --- Complex manifolds --- Connections (Mathematics) --- Pseudogroups --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Global analysis (Mathematics) --- Lie groups --- Geometry, Differential --- Analytic spaces --- Manifolds (Mathematics) --- Adjunction formula. --- Affine connection. --- Affine transformation. --- Algebraic surface. --- Algebraic torus. --- Algebraic variety. --- Analytic continuation. --- Analytic function. --- Automorphic function. --- Automorphism. --- Bilinear form. --- Canonical bundle. --- Characterization (mathematics). --- Cohomology. --- Compact Riemann surface. --- Complex Lie group. --- Complex analysis. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex number. --- Complex plane. --- Complex torus. --- Complex vector bundle. --- Contraction mapping. --- Covariant derivative. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential form. --- Differential geometry. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Elliptic operator. --- Elliptic surface. --- Enriques surface. --- Equation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exterior derivative. --- Fiber bundle. --- General linear group. --- Geometric genus. --- Group homomorphism. --- Hausdorff space. --- Holomorphic function. --- Homomorphism. --- Identity matrix. --- Invariant subspace. --- Invertible matrix. --- Irreducible representation. --- Jacobian matrix and determinant. --- K3 surface. --- Kähler manifold. --- Lie algebra representation. --- Lie algebra. --- Line bundle. --- Linear equation. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Manifold. --- Mathematical analysis. --- Mathematical induction. --- Ordinary differential equation. --- Partial differential equation. --- Permutation. --- Polynomial. --- Principal bundle. --- Projection (linear algebra). --- Projective connection. --- Projective line. --- Pseudogroup. --- Quadratic transformation. --- Quotient space (topology). --- Representation theory. --- Riemann surface. --- Riemann–Roch theorem. --- Schwarzian derivative. --- Sheaf (mathematics). --- Special case. --- Subalgebra. --- Subgroup. --- Submanifold. --- Symmetric tensor. --- Symmetrization. --- Tangent bundle. --- Tangent space. --- Tensor field. --- Tensor product. --- Tensor. --- Theorem. --- Topological manifold. --- Uniformization theorem. --- Uniformization. --- Unit (ring theory). --- Vector bundle. --- Vector space. --- Fonctions de plusieurs variables complexes --- Variétés complexes

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Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Algebraic geometry --- Geometry, Algebraic. --- Homology theory. --- Functions, Zeta. --- Zeta functions --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Geometry --- Abelian category. --- Additive map. --- Adjoint functors. --- Adjunction (field theory). --- Adjunction formula. --- Alexander Grothendieck. --- Algebra homomorphism. --- Artinian. --- Automorphism. --- Axiom. --- Banach space. --- Base change map. --- Base change. --- Betti number. --- Calculation. --- Cartesian product. --- Category of abelian groups. --- Characteristic polynomial. --- Characterization (mathematics). --- Closed immersion. --- Codimension. --- Coefficient. --- Cohomology. --- Cokernel. --- Commutative diagram. --- Commutative property. --- Commutative ring. --- Compact space. --- Corollary. --- Crystalline cohomology. --- De Rham cohomology. --- Degeneracy (mathematics). --- Derived category. --- Diagram (category theory). --- Differential operator. --- Discrete valuation ring. --- Divisibility rule. --- Dual basis. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Epimorphism. --- Equation. --- Equivalence of categories. --- Exact sequence. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exponential type. --- Exterior algebra. --- Exterior derivative. --- Formal power series. --- Formal scheme. --- Frobenius endomorphism. --- Functor. --- Fundamental theorem. --- Hasse invariant. --- Hodge theory. --- Homotopy. --- Ideal (ring theory). --- Initial and terminal objects. --- Inverse image functor. --- Inverse limit. --- Inverse system. --- K-theory. --- Leray spectral sequence. --- Linear map. --- Linearization. --- Locally constant function. --- Mapping cone (homological algebra). --- Mathematical induction. --- Maximal ideal. --- Module (mathematics). --- Monomial. --- Monotonic function. --- Morphism. --- Natural transformation. --- Newton polygon. --- Noetherian ring. --- Noetherian. --- P-adic number. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Projective module. --- Scientific notation. --- Series (mathematics). --- Sheaf (mathematics). --- Sheaf of modules. --- Special case. --- Spectral sequence. --- Subring. --- Subset. --- Symmetric algebra. --- Theorem. --- Topological space. --- Topology. --- Topos. --- Transitive relation. --- Universal property. --- Zariski topology. --- Geometrie algebrique --- Topologie algebrique --- Varietes algebriques --- Cohomologie