Lang S. — Introduction to Algebraic and Abelian Functions :: Электронная библиотека попечительского совета мехмата МГУ

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Lang S. — Introduction to Algebraic and Abelian Functions

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Название: Introduction to Algebraic and Abelian Functions

Автор: Lang S.

Аннотация:

This short book gives an introduction to algebraic and abelian functions, with emphasis on the complex analytic point of view. It could be used for a course or seminar addressed to second year graduate students.
The goal is the same as that of the first edition, although 1 have made a number of additions. I have used the Weil proof of the Riemann-Roch theorem since it is efficient and acquaints the reader with adeles, which are a very useful tool pervading number theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1982

Количество страниц: 171

Добавлена в каталог: 22.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abel — Jacobi theorem      59
Abel's theorem      58
Abelian function      97
Abelian manifold      108 118
Abelian variety      118
Admissible pair      39 41
Admissible Riemann form      151
Algebraic equivalence      103 121
Analytic representation      111
Associated character      121
Canonical class      13
Canonical divisor      13
Canonical involution      144
Cauchy's theorem      53
Chinese remainder theorem      3
Commensurable      149
Compatible pairs (for a divisor)      156
Complete non-singular curve      34
Complete reducibility      117
Complex representation      111
Constant field      5
Curve      5
Degenerate theta function      89
Degree      6
Derivation      14
Differential      11
Differential forms      16
Differential, exact      29
Differential, first kind (dfk)      26 54
Differential, meromorphic      51
Differential, second kind (dsk)      29 61
Differential, third kind (dtk)      29 61
Differentials on Fermat curve      32
Divisor classes      34
Divisor classes on Fermat curve      43
Divisor of differential      13 25
Divisor on $C^{n}$       156
Divisor on abelian manifold      98
Divisor on curve      16
Duality      53 67—71 122—123
Equivalent pairs      42
Exact differential      29
Fermat curve      36 43 72 77
First kind      26 54
Frobenius basis      91
Frobenius decomposition      91
Frobenius theorem      93
Function field      2 5 97
Genus      11
Genus formula      26
Holomorphic differential      52
Homology      53 71 127
Hurwitz formula      26
Ideal      149
Indefinite quaternion algebra      147
Integration      51 56
Involution      120 143 146
Isogeny      116
Isomorphism class of abelian manifold      138 154
Jacobi's theorem      63
Jacobian      59
Kummer pairing      125
Lattice      83 148
Lefschetz Theorem      105

Left order      148
Lies above      2
Linear system      98 104
Linearly equivalent      6 99
Local parameter      16 31
Logarithm symbol      73
Meromorphic differential      51
Non-degenerate theta function      92 99
Non-degenerate vector      149
Non-special      63
Norm      143
Normalized theta function      87 138
Order      1 6
Order (ring)      148
p-adic representation      115
Parallelotope      11
PARAMETER      16 31 47
periods      55 127
Periods on Fermat curve      72 77
Periods on universal covering space      75
Pfaffian      90
Picard group      103 121
Place      1 31
Poincare's theorem      117
Point      5
Polarization      135
Pole      1 46
Positive divisor      6
Prime      5
Principal polarization      136
Projective embedding      105
Quadratic character      87
Quaternion algebra      143
Quaternion type      150
Ramification      1
Rational map      112
Rational point      46
Reduced norm      143
Reduced pfaffian      96
Residue      17 21
Riemann form      90 131 151
Riemann matrices      131
Riemann Relations      66 134
Riemann surface      46
Riemann — Roch theorem      5
Riemann — Roch theorem on the torus      99
Rohrlich theorem      79
Second kind      29 61
Simple point      31
Simple torus      117
Subtorus      116
Sum of residues      21
Tate group      113
Theta function      83
Theta function, associated with divisor      157
Third kind      29 61
Trace      143
Translation of theta function      101
Trivial derivation      14
TYPE      92 151
UNIT      73
Universal covering space      75
Unramified      2
Value      1

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