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Forms of the rings R[X] and R[X, Y]

1972
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Glasgow Mathematical Journal
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Let R be a ring and let S = Spec/?. Let us consider the Etalefini topology on S [5] . By a form of a given S-scheme T we mean any affine 5-scheme W that is locally (in the etalefini topology) isomorphic to T. We shall consider forms of the J?-schemes T= SpecR [X] and In the case where R = k is a field, the above definition gives the classical definition of forms of A:-algebras [2]. The problem of determining the forms of k[X] is easy. If A is a A>algebra such that, for some separable extension

doi:10.1017/s0017089500001464
fatcat:ndsar6zslncnpcb4yx34snyo4a