LEADER 04712nam  22013335  450 
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010   $a1-4008-8247-8
024 7 $a10.1515/9781400882472
035   $a(CKB)3710000000631361
035   $a(MiAaPQ)EBC4738733
035   $a(DE-B1597)468018
035   $a(OCoLC)979743327
035   $a(DE-B1597)9781400882472
035   $a(EXLCZ)993710000000631361
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aLectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 /$fGerd Faltings
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1992
215   $a1 online resource (113 pages)
225 0 $aAnnals of Mathematics Studies ;$v309
311   $a0-691-08771-7 
311   $a0-691-02544-4 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tTABLE OF CONTENTS -- $tINTRODUCTION -- $tLIST OF SYMBOLS -- $tLECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- $tLECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- $tLECTURE 3. LAPLACIANS AND HEAT KERNELS -- $tLECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- $tLECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- $tLECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- $tLECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- $tREFERENCES
330   $aThe arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
410  0$aAnnals of mathematics studies ;$vno. 127.
606   $aGeometry, Algebraic
606   $aRiemann-Roch theorems
610   $aAddition.
610   $aAdjoint.
610   $aAlexander Grothendieck.
610   $aAlgebraic geometry.
610   $aAnalytic torsion.
610   $aArakelov theory.
610   $aAsymptote.
610   $aAsymptotic expansion.
610   $aAsymptotic formula.
610   $aBig O notation.
610   $aCartesian coordinate system.
610   $aCharacteristic class.
610   $aChern class.
610   $aChow group.
610   $aClosed immersion.
610   $aCodimension.
610   $aCoherent sheaf.
610   $aCohomology.
610   $aCombination.
610   $aCommutator.
610   $aComputation.
610   $aCovariant derivative.
610   $aCurvature.
610   $aDerivative.
610   $aDeterminant.
610   $aDiagonal.
610   $aDifferentiable manifold.
610   $aDifferential form.
610   $aDimension (vector space).
610   $aDivisor.
610   $aDomain of a function.
610   $aDual basis.
610   $aE6 (mathematics).
610   $aEigenvalues and eigenvectors.
610   $aEmbedding.
610   $aEndomorphism.
610   $aExact sequence.
610   $aExponential function.
610   $aGeneric point.
610   $aHeat kernel.
610   $aInjective function.
610   $aIntersection theory.
610   $aK-group.
610   $aLevi-Civita connection.
610   $aLine bundle.
610   $aLinear algebra.
610   $aLocal coordinates.
610   $aMathematical induction.
610   $aMorphism.
610   $aNatural number.
610   $aNeighbourhood (mathematics).
610   $aParameter.
610   $aProjective space.
610   $aPullback (category theory).
610   $aPullback (differential geometry).
610   $aPullback.
610   $aRiemannian manifold.
610   $aRiemann?Roch theorem.
610   $aSelf-adjoint operator.
610   $aSmoothness.
610   $aSobolev space.
610   $aStochastic calculus.
610   $aSummation.
610   $aSupertrace.
610   $aTheorem.
610   $aTransition function.
610   $aUpper half-plane.
610   $aVector bundle.
610   $aVolume form.
615  0$aGeometry, Algebraic.
615  0$aRiemann-Roch theorems.
676   $a516.3/5
700   $aFaltings$b Gerd, $059811
701   $aZhang$b Shouwu$01195550
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154744103321
996   $aLectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127$92864903
997   $aUNINA