Abstract
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.
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© 2007 Birkhäuser Verlag AG
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(2007). Category theory in Algebraic Geometry. In: Tool and Object. Science Networks. Historical Studies, vol 32. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7524-9_4
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DOI: https://doi.org/10.1007/978-3-7643-7524-9_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7523-2
Online ISBN: 978-3-7643-7524-9
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