Mathematical and Philosophical Legacy of Alexander Grothendieck

Preface.- Grothendieck's 40 Main Years (1949-1991).- Grothendieck and Differential Equations.- The Birkho-Grothendieck Theorem.- In nite Products, Congruent Numbers.- The Enduring Legacy of Grothenedieck's Duality Theorem.- Conjectures and Counterexamples in Grothendieck's Work in Functional Analysis.- Tohoku 60 years after.- About Grothendieck Fibrations.-Grothendieck did not Believe in Universes, He believed in Topos and Schemes.- Motivating Motives.- My View on and Experience with Grothendieck's Anabelian Geometry.- Grothendieck's Use of Equality.- Towards a Geometry for Syntax.- Boolean Valued Models, Sheafifications, and Boolean Ultrapowers of Tychono Spaces.- Investigating De nability in Propositional Logic.- Grothendieck and Model Theory.- Context-Dependence and Descent Theory.- Grothendieck and Teichmueller Modular Spaces.

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• Fundamentos da Matemática
• História da Matemática
• Álgebra
• Geometria algébrica
• Teoria dos números
• Lógica matemática

Alexander Grothendieck;Weil Conjectures;Homotopy Hypothesis;Category Theory;Nuclear Spaces;Derived Categories