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which generalizes it: a formal holomorphic function on a variety is essentially just a section of the structure sheaf of a related formal scheme.
161:
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Zariski, Oscar (1949), "A fundamental lemma from the theory of holomorphic functions on an algebraic variety",
36:. They are sometimes just called holomorphic functions when no confusion can arise. They were introduced by
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Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields
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The theory of formal holomorphic functions has largely been replaced by the theory of
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are defined by gluing together holomorphic functions on affine subvarieties.
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In general holomorphic functions along a subvariety
67:is an affine subvariety of the affine variety
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83:, then a formal holomorphic function along
87:is just an element of the completion of
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140:, Mem. Amer. Math. Soc., vol. 5,
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1:
32:defined in a neighborhood of
28:is an algebraic analog of a
18:formal holomorphic function
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16:In algebraic geometry, a
118:Ann. Mat. Pura Appl. (4)
24:of an algebraic variety
136:Zariski, Oscar (1951),
75:of the coordinate ring
71:defined by an ideal
30:holomorphic function
20:along a subvariety
162:Algebraic geometry
38:Oscar Zariski
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53:formal schemes
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124:: 187–198,
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59:Definition
156:Category
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46:1951
42:1949
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79:of
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158::
142:MR
126:MR
122:29
120:,
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104:W
100:V
93:I
89:R
85:V
81:W
77:R
73:I
69:W
65:V
34:V
26:W
22:V
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