LEADER 03422nam 2200565 450 001 9910827875203321 005 20170816143334.0 010 $a1-4704-0158-4 035 $a(CKB)3360000000464757 035 $a(EBL)3113880 035 $a(SSID)ssj0000888774 035 $a(PQKBManifestationID)11487560 035 $a(PQKBTitleCode)TC0000888774 035 $a(PQKBWorkID)10866809 035 $a(PQKB)11704252 035 $a(MiAaPQ)EBC3113880 035 $a(RPAM)1618215 035 $a(PPN)195414551 035 $a(EXLCZ)993360000000464757 100 $a20140905h19961996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn arithmetic Riemann-Roch theorem for singular arithmetic surfaces /$fWayne Aitken 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1996. 210 4$dİ1996 215 $a1 online resource (189 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 120, Number 573 300 $a"March 1996, volume 120, number 573 (first of 4 numbers)." 311 $a0-8218-0407-3 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Chapter 1. The Intersection Pairing for One-Dimensional Schemes""; ""1. Preliminaries""; ""2. The Determinant of Cohomology Functor""; ""3. The Norm Functor for Zero-Dimensional Schemes""; ""4. The Definition of the Intersection Pairing""; ""5. The Intersection Pairing and Norms""; ""6. The Norm Functor for Divisors""; ""7. Other Properties of the Intersection Pairing""; ""8. Extensions of the Base Field""; ""Chapter 2. The Intersection Pairing for Families of One-dimensional Schemes""; ""1. Introduction""; ""2. Horizontal Divisors""; ""3. The Norm Functor"" 327 $a""4. The Intersection Pairing""""5. The Determinant of Cohomology Line Bundle""; ""6. Flat Base Change""; ""Chapter 3. The Riemann-Roch Isomorphism""; ""1. The Relative Dualizing Sheaf""; ""2. The Adjunction Formula""; ""3. The Duality Isomorphism on Determinants""; ""4. The Riemann-Roch Isomorphism""; ""Chapter 4. Intersection Functions on Complex Curves""; ""1. Motivation: The Non-Archimedean Situation""; ""2. The Archimedean Case: Basic Definitions""; ""3. Intersection Functions on Nonsingular Curves""; ""4. Intersection Functions on Singular Curves: The Existence Theorem"" 327 $a""5. Classification of Intersection Functions: Preliminaries""""6. Classification of Intersection Functions""; ""7. Chern Forms of Intersection Functions""; ""8. Chern Forms of Intersection Functions: Proofs""; ""9. Chern Forms of Intersection Functions: Another Interpretation""; ""Chapter 5. The Arithmetic Riemann-Roch Isomorphism""; ""1. Norms for Determinants of Cohomology""; ""2. The Riemann-Roch Isomorphism for Arithmetic Surfaces""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 120, Number 573. 606 $aArithmetical algebraic geometry 606 $aRiemann-Roch theorems 615 0$aArithmetical algebraic geometry. 615 0$aRiemann-Roch theorems. 676 $a512/.74 700 $aAitken$b Wayne$f1963-$01606333 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827875203321 996 $aAn arithmetic Riemann-Roch theorem for singular arithmetic surfaces$93932083 997 $aUNINA