Analytic sheaves in Banach spaces☆

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.

Bounded analytic sets in Banach spaces

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Douady ’ S Conjecture on Banach Analytic Spaces

We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banach spaces.

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...

Analytic approximations of norms in separable Banach spaces