# The affine part of the Picard scheme

## TL;DR

This paper characterizes the structure of the Picard scheme by describing its maximal torus and unipotent subgroup for proper schemes over perfect fields, enhancing understanding of its algebraic group components.

## Contribution

It provides a detailed description of the affine parts of the Picard scheme, specifically the maximal torus and unipotent subgroup, which was not previously explicitly characterized.

## Key findings

- Identifies the maximal torus of the Picard scheme.
- Describes the maximal unipotent subgroup of the Picard scheme.
- Clarifies the structure of the Picard scheme over perfect fields.

## Abstract

We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.