Doctor of Philosophy
The derived category of coherent sheaves on a smooth projective variety is an important object of study in algebraic geometry. One important device relevant for this study is the notion of tilting sheaf.
This thesis is concerned with the existence of tilting sheaves on some smooth projective varieties. The main technique we use in this thesis is Galois descent theory. We first construct tilting bundles on general Brauer-Severi varieties. Our main result shows the existence of tilting bundles on some Brauer-Severi schemes. As an application, we prove that there are tilting bundles on an arithmetic toric variety whose toric variety has a splitting fan.
Yan, Youlong, "Tilting Sheaves on Brauer-Severi Schemes and Arithmetic Toric Varieties" (2014). Electronic Thesis and Dissertation Repository. 2312.