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

TL;DR

This mathematical monograph presents algebraization and purity theorems that establish Lefschetz-type results for fundamental and Picard groups, updating the classic SGA 2 text.

Contribution

It provides new proofs and perspectives on Lefschetz theorems using algebraization and purity, enhancing the understanding of fundamental and Picard groups.

Findings

Proves algebraization theorems for coherent sheaves

Establishes purity theorems in algebraic geometry

Derives Lefschetz theorems for fundamental and Picard groups

Abstract

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.