Lefschetz theorems in flat cohomology and applications

TL;DR

This paper extends Lefschetz theorems to flat cohomology with finite group schemes, leading to new results for Picard schemes and advancing understanding in algebraic geometry.

Contribution

It proves a Lefschetz hyperplane theorem for fppf cohomology with finite group scheme coefficients, a novel generalization in algebraic geometry.

Findings

Lefschetz hyperplane theorem established for fppf cohomology

New Lefschetz results obtained for Picard schemes

Advances in understanding flat cohomology in algebraic geometry

Abstract

We prove a version of the Lefschetz hyperplane theorem for fppf cohomology with coefficients in any finite commutative group scheme over the ground field. As consequences, we establish new Lefschetz results for the Picard scheme.