Abstract
In this chapter we develop sheaf theory only as far as is necessary for later function theoretic applications.
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A subset T of a commutative ring B with unit 1 is called multiplicative if 1 € T and, whenever a, b € T, ab € T. Every multiplicative set T ⊂ B determines the ring of quotients B T whose elements are the equivalence classes of the following equivalence relation on B x T: Two pairs (b i, t i) ∈ B x T are called equivalent if there exists a t ∈ T so that t(t 2 b l — t 1 b 2) = 0. One writes each equivalence class as a “fraction” b/t and carries out the arithmetic operations in the usual way.
Finite holomorphic maps are studied in detail in Chapter I.
A functor T on a category in which the morphisms α: A → A’ and β: A→ A’ can be added is called additive if, for all such morphisms with T-images Tα: TA→ TA’ Tβ: TA→ TA’, it always follows that T(α + β) = Tα + Tβ.
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© 2004 Springer-Verlag Berlin Heidelberg
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Grauert, H., Remmert, R. (2004). Sheaf Theory. In: Theory of Stein Spaces. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18921-0_1
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DOI: https://doi.org/10.1007/978-3-642-18921-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00373-1
Online ISBN: 978-3-642-18921-0
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