×

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)
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Artin, M.: The implicit function theorem in algebraic geometry. Interscience colloquium in algebraic geometry. Bombay 1968 (Oxford University Press).
[2] Auslander, M.: On the dimension of modules and algebras. III. Nagoya Math. J.9, 67-77 (1955). · Zbl 0067.27103
[3] ?, Buchsbaum, D.: Homological dimension in Noetherian rings. II. Trans. Am. Math. Soc.88, 194-206 (1958). · Zbl 0082.03402
[4] Bass, H.: Finitistic dimension and a homological generalization of semi-primary rings. Trans. Am. Math. Soc.95, 466-488 (1960). · Zbl 0094.02201 · doi:10.1090/S0002-9947-1960-0157984-8
[5] ?: Injective dimension in Noetherian rings. Trans. Am. Math. Soc.102, 18-29 (1962). · Zbl 0126.06503 · doi:10.1090/S0002-9947-1962-0138644-8
[6] ?: Big projective modules are free. Illinois J. of Math.7, 23-31 (1963). · Zbl 0115.26003
[7] Ferrand, D.: Descente de la platitude par un homomorphisme fini. C.R.A.S.246, 946-949 (1969). · Zbl 0185.10001
[8] Goblot, R.: Sur deux classes de catégories de Grothendieck. Thèse (à paraître).
[9] EGA: Grothendieck, A., Dieudonné, J., Eléments de géométric algébrique. Publ. Math. I.H.E.S. 4, 8, 11, 17, 20, 24, 28, 32.
[10] SGA: Grothendieck, A., Séminaire de géométrie algébrique (I.H.E.S.).
[11] Grothendieck, A.: Séminaire Bourbaki, exposé 221.
[12] Jensen, C. U.: On the vanishing of \(\mathop {\lim }\limits_ \leftarrow ^{(i)} \) . J. of Algebra15, 151-166 (1970). · Zbl 0199.36202 · doi:10.1016/0021-8693(70)90071-2
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.