Category theory in Algebraic Geometry

Part of the Science Networks. Historical Studies book series (SNHS, volume 32)


In the sequel to his work on sheaf cohomology, Grothendieck in the period 1958–1970 undertakes a complete renewal of the conceptual bases of algebraic geometry. CT intervenes at every stage of this conceptual work, for instance in the introducion of the fundamental concepts of scheme and topos and in important characteristics of Grothendieck’s methodology (descent, relativization). All these innovations are tested, for instance, in the case of the so-called Weil conjectures, but in this case, Grothendieck’s approach yielded only partial results.


Topological Space Algebraic Geometry Prime Ideal Category Theory Nilpotent Element 
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© Birkhäuser Verlag AG 2007

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