Finite flat commutative group schemes embed locally into abelian schemes

Let \(G\) be a finite flat commutative group scheme over a fixed locally noetherian base scheme \(S\). In this brief note, I want to explain the proof of the following theorem due to Raynaud.

Theorem. There exists, Zariski-locally on \(S\), an abelian scheme \(A\) such that \(G\) embeds as a closed \(S\)-subgroup of …

The torsion component of the Picard scheme

This post is a continuation of Sean Cotner’s most recent post [see An example of a non-reduced Picard scheme]. Since writing that post, Bogdan Zavyalov shared some notes of his proving the following strengthened version of the results described there.

Main Theorem. Let \(S\) be a noetherian local ring and …