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Critères de platitude et de projectivité. Techniques de ”platification” d’un module. (Criterial of flatness and projectivity. Technics of ”flatification of a module.). (French) Zbl 0227.14010


MSC:

14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc.
13C11 Injective and flat modules and ideals in commutative rings
14F20 Étale and other Grothendieck topologies and (co)homologies
13J15 Henselian rings
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)

References:

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[11] Grothendieck, A.: Séminaire Bourbaki, exposé 221.
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[13] Kaplansky, I.: Projective modules. Annals of Math.68, 372-377 (1958). · Zbl 0083.25802 · doi:10.2307/1970252
[14] Knutson, D.: Algebraic spaces. Thèse M. I. T. Lectures Notes N{\(\deg\)} 203. Berlin-Heidelberg-New York: Springer 1971.
[15] Lazard, D.: Thèse (=Autour de la platitude). Bull. S. M. F.97, 81-128 (1969); et: Disconnexités des spectres d’anneaux et des préschémas. Bull. S.M.F.95, 95-108 (1967).
[16] Murre, J. P.: Representation of unramified functors. Séminaire Bourbaki, exposé 294.
[17] Olivier, J.-P.: Thèse (à paraître).
[18] Osofsky, B. L.: Homological dimension and the continuum hypothesis. Trans. Am. Math. Soc.132, 217-230 (1968). · Zbl 0157.08201 · doi:10.1090/S0002-9947-1968-0224606-4
[19] Raynaud, M.: Anneaux henséliens. Lecture notes, n{\(\deg\)} 169. Berlin-Heidelberg-New York: Springer 1970.
[20] Warfield, R. B.: Purity and algebraic compactness for modules. Pacific J. of Math.28, 699-719 (1969). · Zbl 0172.04801
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