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 
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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 numbertheoretic 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 BrillNoetherPetri 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 higherdimensional classification theory by Mori and his coworkers (see Kollar [1987]).
No one can doubt the success and potency of the schemetheoretic 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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