In this chapter we study one of the central technical tools of algebraic geometry: If S is a scheme and X and Y are S-schemes we define the product X × S Y of X and Y over S which is also called fiber product. We do this by defining X × S Y as an S-scheme which satisfies a certain universal property (and by proving that such a scheme always exists).
KeywordsBase Change Open Covering Group Scheme Fiber Product Closed Subscheme
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