# On the K-theory of weighted projective curves

## TL;DR

This paper explores the K-theory of weighted smooth projective curves, extending classical divisor theory, Euler form, and Riemann-Roch to the weighted and orbifold context over algebraically closed fields.

## Contribution

It provides a comprehensive, self-contained account of K-theory for weighted projective curves, including new treatments of orbifold Euler characteristic and related invariants.

## Key findings

- Extended divisor theory to weighted curves
- Derived weighted Euler form and Riemann-Roch theorem
- Analyzed orbifold Euler characteristic in this setting

## Abstract

We present a largely self contained account on the K-theory of a weighted smooth projective curve over an algebraically closed field. In particular, we discuss the weighted version of divisor theory, Euler form, and Riemann-Roch theorem. This includes a treatment of the orbifold Euler characteristic.