Lectures on the Arithmetic Riemann-Roch Theorem
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A01=Gerd Faltings
Addition
Adjoint
Alexander Grothendieck
Algebraic geometry
Analytic torsion
Arakelov theory
Asymptote
Asymptotic expansion
Asymptotic formula
Author_Gerd Faltings
Big O notation
Cartesian coordinate system
Category=PBF
Category=PBK
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
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
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
Pullback (category theory)
Pullback (differential geometry)
Riemann-Roch theorem
Riemannian manifold
Self-adjoint operator
Smoothness
Sobolev space
Stochastic calculus
Summation
Supertrace
Theorem
Transition function
Upper half-plane
Vector bundle
Volume form
Product details
- ISBN 9780691025445
- Weight: 170g
- Dimensions: 152 x 229mm
- Publication Date: 10 Mar 1992
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
