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arxiv: math/0511279 · v1 · submitted 2005-11-10 · 🧮 math.AG · math.AC

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Cohomologie locale des faisceaux coh\'erents et th\'eor\`emes de Lefschetz locaux et globaux (SGA 2)

Alexander Grothendieck (IHES , Bures) , Michele Raynaud (Univ. Tours)
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classification 🧮 math.AG math.AC
keywords emeslefschetzcohomologieerentsfaisceauxglobauxgrouplocale
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New updated edition by Yves Laszlo of the book ``Cohomologie locale des faisceaux coh\'erents et th\'eor\`emes de Lefschetz locaux et globaux (SGA 2)'', Advanced Studies in Pure Mathematics 2, North-Holland Publishing Company - Amsterdam, 1968. Published by the Societe Mathematique de France http://smf.emath.fr/Publications/DocumentsMathematiques/ Original text also available in the LaTeX file. Dans cet ouvrage, on montre des th\'eor\`emes d'alg\'ebrisation et de puret\'e qui permettent d'obtenir des th\'eor\`emes de type Lefschetz pour le groupe fondamental ou de Picard. In this monograph algebraization and purity theorems are proved, providing Lefschetz's theorem for both the fundamental group and the Picard group.

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    Twisted cohomologies are compared across algebraic and analytic varieties with definitions of analytic twisting parameters, computations, reviewed isomorphisms for cohomologous twists, and constraints for algebraic de...