Moišezon spaces and positive coherent sheaves

Coherent Sheaves and Cohesive Sheaves

We consider coherent and cohesive sheaves of O–modules over open sets Ω ⊂ Cn. We prove that coherent sheaves, and certain other sheaves derived from them, are cohesive; and conversely, certain sheaves derived from cohesive sheaves are coherent. An important tool in all this, also proved here, is that the sheaf of Banach space valued holomorphic germs is flat. To Linda Rothschild on her birthday

Describing Coherent Sheaves on Projective Spaces via Koszul Duality

It is well known that there is a close connection between coherent sheaves on a projective space P(V ) where V is a a vector space over a field k, and finitely generated graded modules over the symmetric algebra S(V ). The Bernstein-Gelfand-Gelfand (BGG) correspondence [5] from 1978 relates coherent sheaves on P(V ) with graded modules over the exterior algebra Λ(V ∗) = ⊕Λi(V ∗) where V ∗ is th...

Descent for Coherent Sheaves on Rigid-analytic Spaces

If one assumes k to have a discrete valuation, then descent theory for coherent sheaves is an old result of Gabber. Gabber’s method was extended to the general case by Bosch and Görtz [BG]. Our method is rather different from theirs (though both approaches do use Raynaud’s theory of formal models [BL1], [BL2], we use less of this theory). We think that our approach may be of independent interes...

Coherent Sheaves and Categorical

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...

Sheaves on Spaces 006a