A comparison theorem for semi-abelian schemes over a smooth curve

TL;DR

This paper compares flat cohomology and crystalline syntomic complexes for p-divisible groups and semi-abelian schemes over smooth curves, providing insights into their relationships in algebraic geometry.

Contribution

It introduces a comparison theorem linking flat cohomology and crystalline syntomic complexes for specific algebraic structures over smooth curves.

Findings

Establishes a comparison between flat cohomology and crystalline syntomic complexes.

Applies to p-divisible groups over schemes with finite p-bases.

Extends understanding of semi-abelian schemes over smooth curves.

Abstract

We compare flat cohomology with crystalline syntomic complexes in two cases: 1) $p$-divisible groups over a separated $\mathbb F_p$-scheme with local finite $p$-bases, 2) semi-abelian schemes over a separated irreducible smooth curve.