Chevalley scheme
A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. Let X be a separated integral noetherian scheme, R its function field. If we denote by the set of subrings of R, where x runs through X (when , we denote by ), verifies the following three properties
* For each , R is the field of fractions of M.
* There is a finite set of noetherian subrings of R so that and that, for each pair of indices i,j, the subring of R generated by is an -algebra of finite type.
* If in are such that the maximal ideal of M is contained in that of N, then M=N.
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Chevalley scheme
A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. Let X be a separated integral noetherian scheme, R its function field. If we denote by the set of subrings of R, where x runs through X (when , we denote by ), verifies the following three properties
* For each , R is the field of fractions of M.
* There is a finite set of noetherian subrings of R so that and that, for each pair of indices i,j, the subring of R generated by is an -algebra of finite type.
* If in are such that the maximal ideal of M is contained in that of N, then M=N.
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A Chevalley scheme in algebrai ...... s the second condition above).
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A Chevalley scheme in algebrai ...... tained in that of N, then M=N.
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Chevalley scheme
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