Goldschmidt D.M. — Algebraic Functions and Projective Curves :: Электронная библиотека попечительского совета мехмата МГУ

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Goldschmidt D.M. — Algebraic Functions and Projective Curves

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Название: Algebraic Functions and Projective Curves

Автор: Goldschmidt D.M.

Аннотация:

This is a self-contained introduction to algebraic functions and projective curves. The author covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. The author also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves. The book is based on a graduate course taught by the author.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 179

Добавлена в каталог: 18.11.2004

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Предметный указатель

Absolutely irreducible      54
Adele      43—44 47
Adele, class group      44
Adjoint conditions      143
Adjoint curves      145
Adjoint divisor      141
Adjoint function      143
Bezout's theorem      113
Bombieri, Enrico      151
Canonical map      21
Class number      152
Completion      16—18
Completion of a graded algebra      26
Completion of a module      18
Conductor of a plane curve      144
Conductor, local      80
Conorm      69
Degree      113
Degree of a plane curve      137
Derivation      24
Derivation, extension of      26
Derivation, generalized      27
Different      75—82
Different exponent      76 80
Different inverse      81
Different of an element      78
Different transitivity of      76
Differential form      24 61
Differential form, divisor of      61
Differential form, exact      25
Differential form, module of      24
Differential form, regular      62
Discrete valuation ring      5
Discrete valuation ring, completion of      20—23
Divisor      40
Divisor, canonical      48
Divisor, class group      42 153
Divisor, class group order of      152
Divisor, degree of      41
Divisor, field of definition      75
Divisor, group      41
Divisor, linear equivalence      42
Divisor, partial ordering on      42
Divisor, prime      40
Divisor, prime singular      73
Divisor, principal      41
Divisor, separable prime      57
Divisor, special      47 129
Divisors, splitting field for      75
Dual map      139
Dual plane      136
Elliptic curve      52 122
Elliptic curve, group of      53
Extension, Galois      89—93 169—171
Extension, Kummer      101
Extension, purely inseparable      168
Extension, scalar      72
Extension, separable      26 55 57 166—168
Extension, tamely ramifield      77
Extension, totally ramifield      13 78 91
Extension, transcendental      172
Extension, unramified      12 101
Extension, weakly separable      58
Extension, wildly ramified      77 93
Finite fields      172
Finitepotent map      30
Finitepotent subspace      31
Formal power series      21
Frobenius, map      158
Frobenius, substitution      159
Functional field      40
Functional field, geometric      54
Functional field, singular      88
Generic coordinates      142
Generic line      141
Generic map      142
Genius      47
Genius of a plane curve      143
Goppa codes      65

Gorenstein relations      146
Graded algebra      25 104
Graded ideal      104
Graded module      104
Hasse chain rule      29
Hasse derivative      28 64
Hensel's lemma      19
Hilbert basis theorem      116
Hilbert nullstellensatz      105
Hyperplane in infinity      11
Integral closure      3 4
Intersection divisor      112
Intersection multiplicity      112
Intersection multiplicity of plane curves      137
Jacobian      51 70
Laurent series      22 64
Linearly disjoint      168
Local parameter      5
Nakayama's lemma      3
Newton's algorithm      19
Norm      69 70 164 171
Norm absolute      150
Osculation plane      129
Plane model      110
Primitive element      171
Product formula      45
Projective curve      107
Projective embedding      120 122
Projective map      108-114
Projective map, birational      110
Projective map, canonical      121
Projective map, divisor of      110
Projective map, effective      109
Projective map, natural      110
Projective map, normalized      112
Projective map, singularity of      114
Projective space      103
Projective variety      106
Ramification index      10 14 57
Ramification tame      77
Ramification wild      77
Rational function      107
Residue      34—36
Residue, degree      11 14
Residue, field separable      58
Residue, form      33
Residue, local      64
Residue, theorem      60
Residue, trace formula      35 72
Riemann hypothesis      160
Riemann zeta function      150
Riemann — Hurwitz formula      76
Riemann — Roch theorem      50—51 62 122 129 134 146 153 155
Separating variable      26 27 55
Singularities      114—122
Singularities of a plane curve      120 143 146
Smith normal form      6
Splitting field      73
Stoehr — Voloch theorem      133 158
Strong approximation theorem      51 120 147
Strong fixed point      130
Tangent line      53 138
Tate, John      30 59
Taylor's theorem      64
Trace      79 164—168 171
Trace of differential form      71
Transcendence degree      173
Ultrametric inequality      1
Valuation extension theorem      3 109
Valuation ring      1
Weak approximation theorem      7 71 78 80 82 89
Weierstrass, divisor      126 135
Weierstrass, gap sequence      129
Weierstrass, points      127
Wiel bound      161
Wiel differential      48 60
Wiel, Andre      151 160
wronskian      124
Zariaski closed set      103
Zeta function      150

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