Homomorphisms of Infinitely Generated Analytic Sheaves
نویسنده
چکیده
We prove that every homomorphism O ζ → O ζ , with E and F Banach spaces and ζ ∈ C, is induced by a Hom(E,F )-valued holomorphic germ, provided that 1 ≤ m < ∞. A similar structure theorem is obtained for the homomorphisms of type O ζ → Sζ , where Sζ is a stalk of a coherent sheaf of positive mζ -depth. We later extend these results to sheaf homomorphisms, obtaining a condition on coherent sheaves which guarantees the sheaf to be equipped with a unique analytic structure in the sense of Lempert-Patyi.
منابع مشابه
A counterexample to the Hodge conjecture for Kähler varieties
H(X,C) = ⊕p+q=kH (X). A class α ∈ H(X,Q) is said to be a rational Hodge class if its image in H(X,C) belongs to H(X). As is well known, the classes which are Poincaré dual to irreducible algebraic subvarieties of codimension p of X are degree 2p Hodge classes. The Hodge conjecture asserts that any rational Hodge class is a combination with rational coefficients of such classes. In the case of a...
متن کاملThe separable transfer
The goal of this paper is to give an approach to constructing transfer homomorphisms along such maps π for abelian sheaves and presheaves of spectra which holds generally for the standard geometric topologies on the category Sch|S of schemes of finite type over S, satisfies the usual properties, and specializes to known phenomena. The construction displayed here, called the separable transfer, ...
متن کاملStiefel-whitney Classes for Coherent Real Analytic Sheaves
We develop Stiefel-Whitney classes for coherent real analytic sheaves and investigate their applications to analytic cycles on real analytic manifolds.
متن کاملAnalytic 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.
متن کاملK-theory, Chow groups and Riemann-Roch
1 K and K0 of schemes Let X be a quasi-projective variety. We define K(X) as follows. Let Fvb(X) be the free abelian group on all isomorphism classes of vector bundles (of finite rank) over X and consider the equivalence relation Rvb(X) generated by the following. If 0 → E1 → E2 → E3 → 0 is an exact sequence of vector bundles, then [E2] = [E1] + [E3]. The quotient Fvb(X)/Rvb(X) is called K(X). ...
متن کامل