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 1272864903UNINA05372nam 22009135 450 991039274500332120230125185159.03-030-37606-010.1007/978-3-030-37606-2(CKB)4100000011223418(DE-He213)978-3-030-37606-2(MiAaPQ)EBC6167713(Au-PeEL)EBL6167713(OCoLC)1151408113(oapen)https://directory.doabooks.org/handle/20.500.12854/31176(PPN)259460990(EXLCZ)99410000001122341820200407d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierSecurity in an Interconnected World A Strategic Vision for Defence Policy /edited by Ernst Hirsch Ballin, Huub Dijstelbloem, Peter de Goede1st ed. 2020.ChamSpringer Nature2020Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (X, 183 p. 27 illus., 22 illus. in color.) Research for Policy, Studies by the Netherlands Council for Government Policy,2662-36843-030-37605-2 This open access book follows the idea that security policy must be based on strategic analysis. Defence policy and the role of the armed forces can subsequently be determined on the grounds of said analysis. More than ever, internal and external security, and developments both in the Netherlands and abroad are interconnected. The world order is shifting, the cooperation within NATO and the EU is under pressure and the Dutch armed forces are gasping for breath. What is the task of Dutch security and the defence policy? There have been growing calls in the last few years to end the devastating cuts in the defence budget and to invest more in security. The acute threats and conflicts in which the Netherlands are involved have served as a wake-up call. The shooting down of Flight MH17 over Ukraine, the streams of refugees from Syria and other countries, the conflict with Da’esh in Syria and Iraq, and terrorist threats reveal how events in many of the world’s flash-points have a direct or indirect impact on the Netherlands. Conflicts in other countries have a spill-over effect in The Netherlands. This is illustrated by tensions between population groups and the clashes over the Gülen schools after the failed putsch in Turkey on 15 July 2016 and over the constitutional referendum in that country. How do we ensure that any additional funds are not divided amongst the branches of the armed forces without any sense of strategic direction? What should a future-proof security policy that plots the course of defence policy entail? What strategic analyses should lie behind the political choices that are made? This book answers these questions and offers a comprehensive framework addressing among other things human security, national security and flow security.Research for Policy, Studies by the Netherlands Council for Government Policy,2662-3684International relationsHuman rightsSystem safetyEuropean Economic Community literatureInternational Relationshttps://scigraph.springernature.com/ontologies/product-market-codes/912000Human Rightshttps://scigraph.springernature.com/ontologies/product-market-codes/R19020Security Science and Technologyhttps://scigraph.springernature.com/ontologies/product-market-codes/P31080European Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/W33010International RelationsHuman RightsSecurity Science and TechnologyEuropean Integrationthe interconnected worldonline defence policyinternational relationssecurity science and technologyintegration and technologyDutch defence policiesThe Netherlands' positioning in Europehuman rights in The NetherlandsEuropean integrationOpen AccessInternational relationsHuman rights, civil rightsSecurity & fire alarm systemsEconomic systems & structuresInternational institutionsInternational relations.Human rights.System safety.European Economic Community literature.International Relations.Human Rights.Security Science and Technology.European Integration.327Hirsch Ballin Ernstedt906894Hirsch Ballin Ernstedthttp://id.loc.gov/vocabulary/relators/edtDijstelbloem Huubedthttp://id.loc.gov/vocabulary/relators/edtde Goede Peteredthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910392745003321Security in an Interconnected World3361039UNINA