04712nam 22013335 450 991015474410332120190708092533.01-4008-8247-810.1515/9781400882472(CKB)3710000000631361(MiAaPQ)EBC4738733(DE-B1597)468018(OCoLC)979743327(DE-B1597)9781400882472(EXLCZ)99371000000063136120190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierLectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 /Gerd FaltingsPrinceton, NJ : Princeton University Press, [2016]©19921 online resource (113 pages)Annals of Mathematics Studies ;3090-691-08771-7 0-691-02544-4 Includes bibliographical references.Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- LIST OF SYMBOLS -- LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- LECTURE 3. LAPLACIANS AND HEAT KERNELS -- LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- LECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- REFERENCESThe 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.Annals of mathematics studies ;no. 127.Geometry, AlgebraicRiemann-Roch theoremsAddition.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.Geometry, Algebraic.Riemann-Roch theorems.516.3/5Faltings Gerd, 59811Zhang Shouwu1195550DE-B1597DE-B1597BOOK9910154744103321Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 1272864903UNINA