Pushforwards of Tilting Sheaves

Abstract

We investigate the behaviour of tilting sheaves under pushforward by a finite Galois morphism. We determine conditions under which such a pushforward of a tilting sheaf is a tilting sheaf. We then produce some examples of Severi Brauer flag varieties and arithmetic toric varieties in which our method produces a tilting sheaf, adding to the list of positive results in the literature. We also produce some counterexamples to show that such a pushfoward need not be a tilting sheaf.

21 pages

References in corpus (4)

• A Derived Equivalence for some Twisted Projective Homogeneous Varieties
• Non-existence of exceptional collections on twisted flags and categorical representability via noncommutative motives
• Tilting objects on twisted forms of some relative flag varieties
• No full exceptional collections on non-split Brauer--Severi varieties of dimension $\le 3$