Algebraic Structure of the Restricted Analytic Sheaves and Restricted Ideal Sheaves

Sheaves on Algebraic Stacks

Sheaves on Algebraic Stacks

Sheaves on Algebraic Stacks

Analytic Sheaves in Banach Spaces

We introduce a class of analytic sheaves in a Banach space X, that we shall call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan’s Theorems A and B for cohesive sheaves on pseudoconvex open subsets Ω ⊂ X, provided X has an unconditional basis.

Theory of Non - Lc Ideal Sheaves

We introduce the notion of non-lc ideal sheaves. It is an analogue of the notion of multiplier ideal sheaves. We establish the restriction theorem, which seems to be the most important property of non-lc ideal sheaves.