Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 /

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 enabl...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Faltings, Gerd (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2016]
Colección:Annals of Mathematics Studies ; 127
Temas:
Geometry, Algebraic.
Riemann-Roch theorems.
MATHEMATICS / Geometry / Algebraic.
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.
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