t-structures on elliptic fibrations (Q2374202)

In this paper, the author constructs t-structures on elliptic fibrations coming from the geometry of the variety (a surface or threefold), the fibration, and the dual fibration. Using these, he proposes an alternative to the notion of stability which is better behaved under base change. Finally, he shows that the heart of some of these t-structures are equivalent under a relative Fourier-Mukai transform up to shifting and tilting. These equivalences are proved by filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures. Note, this is to be the first in a series of articles developing these results.