Tate resolutions on toric varieties

Abstract

We develop an analogue of Eisenbud–Fløystad–Schreyer’s Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier–Mukai transform, works quite generally and provides a new perspective on the relationship between Tate resolutions and Beilinson’s resolution of the diagonal. We also develop a Beilinson-type resolution of the diagonal for toric varieties.