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Eisenbud D., Harris J. - Schemes (textbook)

Название: Schemes (textbook)
Автор: Eisenbud D., Harris J.
Категория: Математика
Тип: Книга
Дата: 04.01.2009 12:07:23
Скачано: 45
Описание: What schemes are The theory of schemes is the foundation for algebraic geometry formulated by Alexandre Grothendieck and his many coworkers. It is the basis for a grand unification of number theory and algebraic geometry, dreamt of by number theorists and geometers for over a century. It has strengthened classical algebraic geometry by allowing flexible geometric arguments about infinitesimals and limits in a way that the classic theory could not handle. In both these ways it has made possible astonishing solutions of many concrete problems. On the number-theoretic side one may cite the proof of the Weil conjectures, Grothendieck's original goal (Deligne [1974]) and the proof of the Mordell Conjecture (Faltings [1984]). In classical algebraic geometry one has the development of the theory of moduli of curves, including the resolution of the Brill-Noether-Petri problems, by Deligne, Mumford, Griffiths, and their coworkers (see Harris and Morrison [1998] for an account), leading to new insights even in such basic areas as the theory of plane curves; the firm footing given to the classification of algebraic surfaces in all characteristics (see Bombieri and Mumford [1976]); and the development of higher-dimensional classification theory by Mori and his coworkers (see Kollar [1987]). No one can doubt the success and potency of the scheme-theoretic methods. Unfortunately, the average mathematician, and indeed many a beginner in algebraic geometry, would consider our title, "The Geometry of Schemes", an oxymoron akin to "civil war". The theory of schemes is widely
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