T-structures on elliptic fibrations

TL;DR

This paper studies t-structures on elliptic fibrations, showing how they relate to Fourier-Mukai transforms and providing a framework for understanding derived categories of coherent sheaves in this context.

Contribution

It introduces a new approach to filtering coherent sheaves on elliptic fibrations using torsion pairs associated with t-structures, and describes their behavior under Fourier-Mukai transforms.

Findings

Filtered categories of coherent sheaves are preserved under Fourier-Mukai transforms.

T-structures on elliptic fibrations can be classified via torsion pairs.

Equivalences of t-structures are established through Fourier-Mukai functors.

Abstract

We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures under Fourier-Mukai transforms.