# Recollements and Ladders for weighted projective lines

## TL;DR

This paper develops new categorical tools called recollements and ladders for weighted projective lines, enabling classification and explicit descriptions of their derived and stable categories, advancing understanding in algebraic geometry.

## Contribution

It introduces a novel method using reduction/insertion functors for constructing recollements and ladders in the context of weighted projective lines.

## Key findings

- Classified recollements for coherent sheaves over weighted projective lines
- Explicitly described ladders in derived and stable categories
- Provided new insights into the structure of categories associated with weighted projective lines

## Abstract

In this paper, we construct recollements and ladders for exceptional curves by using reduction/insertion functors due to $p$-cycle construction. As applications to weighted projective lines, we classify recollements for the category of coherent sheaves over a weighted projective line, and give an explicit description of ladders in two different levels: the bounded derived category of coherent sheaves and the stable category of vector bundles.