Harder-Narasimhan Filtrations and K-Groups of an Elliptic Curve

TL;DR

This paper investigates the structure of vector bundles over an elliptic curve, showing that certain subcategories defined via Harder-Narasimhan filtrations share the same K-groups as the entire category, revealing structural invariants.

Contribution

It establishes that specific subcategories of vector bundles on an elliptic curve, characterized by Harder-Narasimhan filtrations, have identical K-groups to the full category.

Findings

Subcategories defined by Harder-Narasimhan filtrations have the same K-groups as the entire category.

The result applies to vector bundles over elliptic curves over algebraically closed fields.

The work links filtration-based subcategories to algebraic K-theory invariants.

Abstract

Let $X$ be an elliptic curve over an algebraically closed field. We prove that some exact sub-categories of the category of vector bundles over $X$, defined using Harder-Narasimhan filtrations, have the same K-groups as the whole category.