# Intersection Sheaves for Abel maps

## TL;DR

This paper develops a variant of intersection sheaves, extending the Deligne pairing, to define Abel maps in rational simple connectedness, and studies related classifying stacks.

## Contribution

It introduces a new construction of intersection sheaves with desirable properties for Abel maps in rational simple connectedness.

## Key findings

- Extended intersection sheaves to broader schemes.
- Defined Abel maps using the new intersection sheaves.
- Analyzed properties of classifying stacks for Abel maps.

## Abstract

Intersection sheaves, i.e., the Deligne pairing, were first introduced by Deligne in the setting of Poincare duality for etale cohomology, and later in his work on the determinant of cohomology. Intersection sheaves were generalized from smooth schemes to Cohen-Macaulay schemes by Elkik, and then beyond Cohen-Macaulay schemes by Munoz-Garcia. To define the Abel maps arising in rational simple connectedness on the natural parameter spaces of rational sections, we need a variant of the construction of Munoz-Garcia that has the good properties of the construction using det and Div. In addition, we prove basic properties of the classifying stacks that arise in the definition of the Abel maps.