Title: Introduction to schemes
Speaker: Diego Chicharro
Abstract: Schemes were introduced by Grothendieck to overcome many of the limitations that classical algebraic varieties have. For example, it is no longer necessary for the base field to be algebraically closed, and in fact it can even be an arbitrary ring, which in particular makes the theory of schemes extremely useful in number theory. On the other hand, allowing nilpotent regular functions makes it possible to count intersection multiplicities easily. In this talk I will introduce schemes in a very gentle way, first reviewing the classical theory and motivating the right notion of “geometric object”. Generalising this will lead us to define schemes in a very natural way.
Some snacks will be provided before and after the talk.
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