Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Cassels J.W.S. — Lectures on Elliptic Curves
Cassels J.W.S. — Lectures on Elliptic Curves



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Lectures on Elliptic Curves

Автор: Cassels J.W.S.

Аннотация:

The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 143

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
"Riemann hypothesis for function fields"      2 119
$H^1$      99
'Hilbert 90'      95 97
Birationally equivalent      4
Birch      71 110 126(fn)
Blichfeldt      19
Bremner      55(fn)
Canonical form      32 et seq
Canonical height      83
Chatelet      108
Chord and tangent processes      24
Coboundary      90
Cobounding      90
Cocycle      90 98
Cocycle (continuous)      101
Cocycle identity      90 98
Cohomology (Galois)      89 et seq
Cohomology group      98 et seq
Complete, completion      8
Continuous (action), (cocycle)      101
Convex (pointset)      18
Cubic curves      23 et seq
Defined over      3
Degenerate (laws)      39 et seq
Deligne      121
Desbores      25(fn) 26 130
Deuring      116
Diophantine geometry      1
Diophantos      1 24
Discriminant      77
Elliptic curve      32
Endomorphism      112 et seq
Everywhere locally      14
Exceptional (point)      24
Fermat      1 55 63
Filtration (p-adic)      48
Finite basis theorem      54 et seq
Finite basis theorem (weak)      55
Forgetful functor      75
FORM      13
Frobenius endomorphism      118
Fueter      52(fn)
Function field      58
Fundamental sequence      7
Galois cohomology      89 et seq 101
General position      29
Generic point      58
Genus      30
Genus 0      4 et seq
Genus 1      30 32
Globally      14
Group law      27 et seq
Hasse      119
Hasse principle      see local-global principle
Height      55 78
Height (canonical)      83
Height (logarithmic)      82
Hensel      43
Homogeneous spaces      see Princicpal homogeneous space
Hypatia      1
Integer (p-adic)      9
Invertible      67
Irreducible (curve)      24; see also Reducible
Isogeny      58
J-invariant      93
Jacobian (of curve of genus 1)      92 et seq 95 107
Kernel of reduction      47
Kolyvagin      111
Lang      120
Lenstra      124 128
Level (of point in p-adic case)      47
Lift      43
Lind      85
Local-global principle      2 13 85
localization      14 103
Locally      14
Logarithmic height      82
Mazur      51
Minkowski      19
Mordell      19
Mordell Theorem, Mordell — Weil Theorem      see finite basis theorem
Multiplicity      23 44
Nagell      34(fn) 52(fn)
Neutral element (of group)      27
Newton      24 43
Non-archimedean      7
Non-singular      24
Nonsense      98 et seq
Norm (map)      66
p-adic filtration      48
p-adic integers      9
p-adic numbers      6
p-adic units      9
p-adic valuation      7
Patch      67
Pole      30
Pollard      124
Principal homogeneous spaces      104 et seq
Rational (point etc.)      3
Rational curve (= curve of genus 0)      3
Reducible (curve)      43(fn); see also Irreducible
Reduction mod p      42 et seq
Reichaxdt      85
Resultant      75 et seq
Riemann — Roch theorem      30
Rubin      111
Schmidt      120
Selmer      87 110
Shafarevich      85
Singular (point)      23
Swinnerton — Dyer      71 110
Symmetric (pointset)      18
Tamagawa number      110
Tare      85 109(fn)
Tate — Shafarevich group      85 109
Torsion      102
Triangle inequality      7
Ultrametric inequality      7
Unit (p-adic)      9
Valuation      6
Valuation (p-adic)      7
van der Corput      19
Weak finite basis theorem      55 66
Weil      1 54 108 119
Weil-Chatelet group      108
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2023
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте