Coherent Sheaves and Categorical

COHERENT SHEAVES AND CATEGORICAL sl2 ACTIONS

We introduce the concept of a geometric categorical sl2 action and relate it to that of a strong categorical sl2 action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl2 action induces a strong categorical sl2 action. This allows one to apply the theory of strong sl2 actions to various geometric situations. Our main e...

Model-theoretic Imaginaries and Coherent Sheaves

Braiding via Geometric Lie Algebra Actions

We introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra. The same proof shows that strong categorical actions in the sense of Khovanov-Lauda and Rouquier also lead to braid group actions. As an example, we construct an action of Artin’s...

DERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS VIA CATEGORICAL sl2 ACTIONS

We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.

Descent Theory for Schemes

We give a complete characterization of the class of quasi-compact morphisms of schemes that are stable effective descent morphisms for the SCHEMESindexed category given by quasi-coherent sheaves of modules.