A Short Introduction to Schemes
نویسنده
چکیده
A while back a topologist friend asked me why the set of prime ideals of a ring deserved to be singled out for study. Another friend, a symplectic geometer, asked why anyone would want to put a scheme structure on the paramaters that classify a type of object (i.e. construct a moduli space). Algebraic geometry does have a reputation for being somewhat impenetrable (and I won’t say it’s undeserved), but there are natural reasons to ask these questions. In this talk I introduce schemes and show how they relate to classical varieties. In particular, I discuss the value of allowing rings with nilpotents, one of the major innovations of scheme
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