Oka coherence theorem
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In mathematics, the Oka coherence theorem, proved by , states that the
sheaf Sheaf may refer to: * Sheaf (agriculture), a bundle of harvested cereal stems * Sheaf (mathematics) In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open s ...
\mathcal_ of
holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex de ...
s on \mathbb^n (and subsequently the sheaf \mathcal_ of holomorphic functions on a
complex manifold In differential geometry and complex geometry, a complex manifold is a manifold with a ''complex structure'', that is an atlas (topology), atlas of chart (topology), charts to the open unit disc in the complex coordinate space \mathbb^n, such th ...
X) is
coherent Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole. More specifically, coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics ...
.In paper it was called the idéal de domaines indéterminés.


See also

*
Cartan's theorems A and B In mathematics, Cartan's theorems A and B are two results mathematical proof, proved by Henri Cartan around 1951, concerning a coherent sheaf on a Stein manifold . They are significant both as applied to Function of several complex variables, seve ...
*
Several complex variables The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space \mathbb C^n, that is, -tuples of complex numbers. The name of the field dealing with the properties ...
*
GAGA In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally b ...
* Oka–Weil theorem *
Weierstrass preparation theorem In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point ''P''. It states that such a function is, up to multiplication by a function not zero at ''P'', a poly ...


Note


References

* * * * * Theorems in complex analysis Theorems in complex geometry {{mathanalysis-stub