Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties.
Weil was motivated by the need for a rigorous theory of correspondences on algebraic curves in positive characteristic, which he used in his proof of the Riemann hypothesis for curves over finite fields.
Weil introduced abstract rather than projective varieties partly so that he could construct the Jacobian of a curve. (It was not known at the time that Jacobians are always projective varieties.) It was some time before anyone found any examples of complete abstract varieties that are not projective.
In the 1950s Weil's work was one of several competing attempts to provide satisfactory foundations for algebraic geometry, all of which were superseded by Grothendieck's development of schemes.
See also
[edit]Ссылки
[ редактировать ]- Рейно, Мишель (1999), «Андре Вейль и основы алгебраической геометрии» (PDF) , Уведомления Американского математического общества , 46 (8): 864–867, MR 1704257
- ван дер Варден, Бартель Леендерт (1971), «Основы алгебраической геометрии от Севери до Андре Вейля», Архив истории точных наук , 7 (3): 171–180, doi : 10.1007/BF00357215 , MR 1554142 , S2CID 189787203
- Вейль, Андре (1946), Основы алгебраической геометрии , Публикации коллоквиума Американского математического общества, том. 29, Провиденс, Род-Айленд: Американское математическое общество , ISBN. 9780821874622 , МР 0023093
- Вейл, Андре (1962), Основы алгебраической геометрии , Публикации коллоквиума Американского математического общества, том. 29 (2-е изд.), Провиденс, Род-Айленд: Американское математическое общество , ISBN. 978-0-8218-1029-3 , МР 0144898
- Зариски, Оскар (1948), «Рецензия на книгу: Основы алгебраической геометрии», Бюллетень Американского математического общества , 54 (7): 671–675, Бибкод : 1948Sci...107...75W , doi : 10.1090/S0002 -9904-1948-09040-1 , МР 1565074