Notes on Dimension Theory of Schemes
نویسنده
چکیده
In this expository note, we discuss various aspects of the theory of dimension of schemes, in particular focusing on which hypotheses are necessary in order to insure good behavior, and what sort of pathologies can otherwise arise. References are frequently exercises in disguise (or not in disguise, as the case may be). In particular, because the intended applications are geometric, we will state everything in terms of schemes rather than rings. The primary situation which will guide our discussion will be that of a scheme X of finite type over a Noetherian base scheme B, and manipulation of various closed subschemes Z of X. Dimension refers always to Krull dimension, and recall that in this situation, the codimension of Z in X is defined to be the maximal length of a chain of integral closed subschemes containing Z inside X.
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I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).
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تاریخ انتشار 2006