Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.

Algebraic geometry --- Algebraïsche meetkunde --- Geometry [Algebraic ] --- Géométrie algébrique --- Meetkunde [Algebraïsche ] --- Riemann-Roch theorema's --- Riemann-Roch thoerems --- Theoremes de Riemann-Roch --- Geometry, Algebraic. --- Riemann-Roch theorems. --- Theorems, Riemann-Roch --- Algebraic functions --- Geometry, Algebraic --- Geometry --- Addition. --- Adjoint. --- Alexander Grothendieck. --- Algebraic geometry. --- Analytic torsion. --- Arakelov theory. --- Asymptote. --- Asymptotic expansion. --- Asymptotic formula. --- Big O notation. --- Cartesian coordinate system. --- Characteristic class. --- Chern class. --- Chow group. --- Closed immersion. --- Codimension. --- Coherent sheaf. --- Cohomology. --- Combination. --- Commutator. --- Computation. --- Covariant derivative. --- Curvature. --- Derivative. --- Determinant. --- Diagonal. --- Differentiable manifold. --- Differential form. --- Dimension (vector space). --- Divisor. --- Domain of a function. --- Dual basis. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Embedding. --- Endomorphism. --- Exact sequence. --- Exponential function. --- Generic point. --- Heat kernel. --- Injective function. --- Intersection theory. --- K-group. --- Levi-Civita connection. --- Line bundle. --- Linear algebra. --- Local coordinates. --- Mathematical induction. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Parameter. --- Projective space. --- Pullback (category theory). --- Pullback (differential geometry). --- Pullback. --- Riemannian manifold. --- Riemann–Roch theorem. --- Self-adjoint operator. --- Smoothness. --- Sobolev space. --- Stochastic calculus. --- Summation. --- Supertrace. --- Theorem. --- Transition function. --- Upper half-plane. --- Vector bundle. --- Volume form.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The description for this book, Riemann Surfaces Related Topics (AM-97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM-97), will be forthcoming.

Geometry --- Riemann surfaces --- -517.54 --- Surfaces, Riemann --- Functions --- Congresses --- Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- 517.54 Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- 517.54 --- Riemann, Surfaces de --- Abstract simplicial complex. --- Affine transformation. --- Algebraic curve. --- Algebraic element. --- Algebraic equation. --- Algebraic surface. --- Analytic function. --- Analytic torsion. --- Automorphic form. --- Automorphic function. --- Automorphism. --- Banach space. --- Basis (linear algebra). --- Boundary (topology). --- Bounded set (topological vector space). --- Cohomology ring. --- Cohomology. --- Commutative property. --- Commutator subgroup. --- Compact Riemann surface. --- Complex analysis. --- Complex manifold. --- Conformal geometry. --- Conformal map. --- Conjugacy class. --- Covering space. --- Diagram (category theory). --- Dimension (vector space). --- Divisor (algebraic geometry). --- Divisor. --- Eigenvalues and eigenvectors. --- Equivalence class. --- Equivalence relation. --- Ergodic theory. --- Existential quantification. --- Foliation. --- Fuchsian group. --- Fundamental domain. --- Fundamental group. --- Fundamental polygon. --- Geodesic. --- Geometric function theory. --- Group homomorphism. --- H-cobordism. --- Hausdorff measure. --- Holomorphic function. --- Homeomorphism. --- Homomorphism. --- Homotopy. --- Hyperbolic 3-manifold. --- Hyperbolic manifold. --- Hyperbolic space. --- Infimum and supremum. --- Injective module. --- Interior (topology). --- Intersection form (4-manifold). --- Isometry. --- Isomorphism class. --- Jordan curve theorem. --- Kleinian group. --- Kähler manifold. --- Limit point. --- Limit set. --- Manifold. --- Meromorphic function. --- Metric space. --- Mostow rigidity theorem. --- Möbius transformation. --- Poincaré conjecture. --- Pole (complex analysis). --- Polynomial. --- Product topology. --- Projective variety. --- Quadratic differential. --- Quasi-isometry. --- Quasiconformal mapping. --- Quotient space (topology). --- Radon–Nikodym theorem. --- Ricci curvature. --- Riemann mapping theorem. --- Riemann sphere. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schwarzian derivative. --- Strictly convex space. --- Subgroup. --- Submanifold. --- Surjective function. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological conjugacy. --- Topological space. --- Topology. --- Uniformization theorem. --- Uniformization. --- Uniqueness theorem. --- Unit disk. --- Vector bundle.