From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept

@article{Chorlay2009FromPT,
  title={From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept},
  author={Renaud Chorlay},
  journal={Archive for History of Exact Sciences},
  year={2009},
  volume={64},
  pages={1-73}
}
  • Renaud Chorlay
  • Published 2009
  • Mathematics
  • Archive for History of Exact Sciences
Historical work on the emergence of sheaf theory has mainly concentrated on the topological origins of sheaf cohomology in the period from 1945 to 1950 and on subsequent developments. However, a shift of emphasis both in time-scale and disciplinary context can help gain new insight into the emergence of the sheaf concept. This paper concentrates on Henri Cartan’s work in the theory of analytic functions of several complex variables and the strikingly different roles it played at two stages of… 
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References

SHOWING 1-10 OF 152 REFERENCES
Recensioni/Reviews-Modern Algebra and the Rise of Mathematical Structures
The notion of mathematical structure is among the most pervasive ones in twentieth century mathematics. "Modern algebra and the rise of mathematical structures" describes two stages in the historical
L' émergence du couple local / global dans les théories géométriques : de Bernard Riemann à la théorie des faisceaux (1851-1953)
Since the 1950's, the distinction between "local" and "global" has been used constantly when expounding various fields of mathematics. However, the first writings to make use of the opposition of
History of topology
Abbreviated. Preface. The emergence of topological dimension theory (T. Crilly, D. Johnson). Development of the concept of homotopy (R. Vanden Eynde). Differential forms (V.J. Katz). Weyl and the
Outline of a History of Differential Geometry: I
If the French drew the most consistent economic and political consequences from their revolution, the Germans on the other hand were more profoundly stimulated by the accompanying intellectual
Outline of a History of Differential Geometry (II)
If the French drew the most consistent economic and political consequences from their revolution, the Germans on the other hand were more profoundly stimulated by the accompanying intellectual
Linear Differential Equations and Group Theory from Riemann to Poincare
The origins of the theory of modular and automorphic functions are found in the work of Legendre, Gauss, Jacobi, and Kummer on elliptic functions and the hypergeometric equation. Riemann's work on
Theory of Lie Groups
This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this
Homology With Local Coefficients
In a recent paper [16] the author has had occasion to introduce and use what he believed to be a new type of homology theory, and he named it homology with local coefficients. It proved to be the
The Architecture of Mathematics
1. Mathematic or mathematics? To present a view of the entire field of mathematical science as it exists,-this is an enterprise which presents, at first sight, almost insurmountable difficulties, on
...
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2
3
4
5
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