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

Gerd Faltings (Autor)

eBook Download: PDF

2016
118 Seiten
Princeton University Press (Verlag)
978-1-4008-8247-2 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: 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 • linear algebra • line bundle • Local coordinates • Mathematical Induction • Morphism • Natural number • Neighbourhood (mathematics) • Parameter • projective space • pullback • Pullback (category theory) • Pullback (differential geometry) • 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
• ISBN-10: 1-4008-8247-8 / 1400882478
• ISBN-13: 978-1-4008-8247-2 / 9781400882472