Kohomologiegruppen und Konstantenreduktion in Funktionenk�rpern

Kiyek, Karl-Heinz

doi:10.1007/bf01404551

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1971

1978

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Cited by 3 publications

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“…Remark C above); if f: X-p Spec(R) is obtained by blowing up the m-primary ideal I = I n R, then, since R is flat over R and I IR, we have Xk= X@RR, and it follows easily that f is a desingularization of Spec(R) (cf. beginning of proof of the second Proposition in Section (lb) below; or just use [EGA OIV,(17…”

Section: * * *mentioning

confidence: 99%

Desingularization of Two-Dimensional Schemes

Lipman¹

1978

The Annals of Mathematics

303

181

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1 (*) can be reformulated in numerous tantalizing ways. It is equivalent, for example, to the finite-dimensionality of H'(O0'R) where _5P is the Zariski-Riemann space associated with Y (cf. [17]). It can also be posed as a statement about certain Hilbert-Samuel polynomials in a two-dimensional normal local ring (cf. Remark (B), end of Section (la)). * * * The actual proof of reduction to pseudo-rational singularities is given in Section 3. For reasons explained below, this will not be the proof of (*) just indicated, but a variant which, if less striking, is ultimately shorter * * * This introduction is concluded with some further remarks on the theorem.

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confidence: 99%