TY - BOOK ID - 2435552 TI - Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 AU - Faltings, Gerd, AU - Zhang, Shouwu. PY - 2016 VL - vol 127 SN - 0691087717 0691025444 1400882478 PB - Princeton, NJ : Princeton University Press, DB - UniCat KW - Algebraic geometry KW - Algebraïsche meetkunde KW - Geometry [Algebraic ] KW - Géométrie algébrique KW - Meetkunde [Algebraïsche ] KW - Riemann-Roch theorema's KW - Riemann-Roch thoerems KW - Theoremes de Riemann-Roch KW - Geometry, Algebraic. KW - Riemann-Roch theorems. KW - Theorems, Riemann-Roch KW - Algebraic functions KW - Geometry, Algebraic KW - Geometry KW - Addition. KW - Adjoint. KW - Alexander Grothendieck. KW - Algebraic geometry. KW - Analytic torsion. KW - Arakelov theory. KW - Asymptote. KW - Asymptotic expansion. KW - Asymptotic formula. KW - Big O notation. KW - Cartesian coordinate system. KW - Characteristic class. KW - Chern class. KW - Chow group. KW - Closed immersion. KW - Codimension. KW - Coherent sheaf. KW - Cohomology. KW - Combination. KW - Commutator. KW - Computation. KW - Covariant derivative. KW - Curvature. KW - Derivative. KW - Determinant. KW - Diagonal. KW - Differentiable manifold. KW - Differential form. KW - Dimension (vector space). KW - Divisor. KW - Domain of a function. KW - Dual basis. KW - E6 (mathematics). KW - Eigenvalues and eigenvectors. KW - Embedding. KW - Endomorphism. KW - Exact sequence. KW - Exponential function. KW - Generic point. KW - Heat kernel. KW - Injective function. KW - Intersection theory. KW - K-group. KW - Levi-Civita connection. KW - Line bundle. KW - Linear algebra. KW - Local coordinates. KW - Mathematical induction. KW - Morphism. KW - Natural number. KW - Neighbourhood (mathematics). KW - Parameter. KW - Projective space. KW - Pullback (category theory). KW - Pullback (differential geometry). KW - Pullback. KW - Riemannian manifold. KW - Riemann–Roch theorem. KW - Self-adjoint operator. KW - Smoothness. KW - Sobolev space. KW - Stochastic calculus. KW - Summation. KW - Supertrace. KW - Theorem. KW - Transition function. KW - Upper half-plane. KW - Vector bundle. KW - Volume form. UR - https://www.unicat.be/uniCat?func=search&query=sysid:2435552 AB - 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. ER -