Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2)

By A. Grothendieck, M. Raynaud. 2005

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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 this http URL 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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Citations in the corpus

On space filling curves and Albanese varieties (2001, background): “It follows that G is an abelian variety iff dim(L) = 0 iff the fibre of G over some point of Spec(R) is an abelian variety.”
t-Structures on the Derived Categories of Holonomic D-Modules and Coherent O-Modules (2004, background): “For any M ∈ Dqc(A ), one has an isomorphism ([3]) H n Φ (M) ' lim −→ I ExtnOX (OX/I, M)”
The Galois group of a stable homotopy theory (2014, result): “In order to prove this result, we recall the Zariski–Nagata purity theorem, for which a useful reference is Exposé X of [31].”
Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal (2010, background): “Notice that by Grothendieck-Lefschetz theorem [14], L is the restriction of a line bundle on J ( Y ), hence must be numerically eﬀective, because one can show, again by an inﬁnitesimal variation of Hodge structure argument, that NS( J ( Y )) = Z , for very general Y .”
Proregular sequences, local cohomology, and completion (2003, result): “This corrects several results shown in [1], [8], [9], and [10].”