Quasicoherent sheaves over affine Hensel schemes
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- by Silvio Greco and Rosario Strano PDF
- Trans. Amer. Math. Soc. 268 (1981), 445-465 Request permission
Abstract:
The following two theorems concerning affine Hensel schemes are proved. Theorem A. Every quasi-coherent sheaf over an affine Hensel scheme is generated by its global sections. Theorem B. ${H^p}(X, F) = 0$ for all positive $p$ and all quasi-coherent sheaves $F$ over an affine Hensel scheme $X$.References
- M. Artin, On the joins of Hensel rings, Advances in Math. 7 (1971), 282–296 (1971). MR 289501, DOI 10.1016/S0001-8708(71)80007-5
- N. Bourbaki, Éléments de mathématique. Fascicule XXVIII. Algèbre commutative. Chapitre 3: Graduations, filtrations et topologies. Chapitre 4: Idéaux premiers associés et décomposition primaire, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1293, Hermann, Paris, 1961 (French). MR 0171800
- David A. Cox, Algebraic tubular neighborhoods. I, II, Math. Scand. 42 (1978), no. 2, 211–228, 229–242. MR 512271, DOI 10.7146/math.scand.a-11749 —, Algebraic tubular neighborhoods. II, Math. Scand. 42 (1978), 229-243.
- James Dugundji, Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original. MR 0478089
- Roger Godement, Topologie algébrique et théorie des faisceaux, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1252, Hermann, Paris, 1958 (French). Publ. Math. Univ. Strasbourg. No. 13. MR 0102797 A. Grothendieck and J. Dieudonné, Eléments de géométrie algébrique. I, Springer-Verlag, Berlin, 1971. —, Eléments de géométrie algébrique. II, Inst. Hautes Étude Sci. Publ. Math., no. 8, 1961. —, Eléments de géométrie algébrique. III, Inst. Hautes Étude Sci. Publ. Math., no. 11, 1961.
- S. Greco, Anelli henseliani, Categories and commutative algebra (Centro Internaz. Mat. Estivo (C.I.M.E.), III Ciclo, Varenna, 1971) Edizioni Cremonese, Rome, 1973, pp. 41–71 (Italian). MR 0366915
- Silvio Greco, Sulla nozione di preschema henseliano, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 50 (1971), 118–121 (Italian, with English summary). MR 313322
- Silvio Greco, Sul sollevamento dei rivestimenti étale, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971) Academic Press, London, 1973, pp. 67–80 (Italian). MR 0349678
- Laurent Gruson, Une propriété des couples henséliens, Colloque d’Algèbre Commutative (Rennes, 1972) Publ. Sém. Math. Univ. Rennes, Année 1972, Univ. Rennes, Rennes, 1972, pp. 13 (French). MR 0412187
- Silvio Greco and Rosario Strano, Theorems A and B for Henselian schemes, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 67 (1979), no. 1-2, 95–98 (1980) (English, with Italian summary). MR 617282
- Robin Hartshorne, Cohomological dimension of algebraic varieties, Ann. of Math. (2) 88 (1968), 403–450. MR 232780, DOI 10.2307/1970720 —, Algebraic geometry, Springer-Verlag, Berlin, 1977.
- Heisuke Hironaka, Formal line bundles along exceptional loci, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 201–218. MR 0262249
- H. Kurke, G. Pfister, and M. Roczen, Henselsche Ringe und algebraische Geometrie, Mathematische Monographien, Band II, VEB Deutscher Verlag der Wissenschaften, Berlin, 1975 (German). MR 0491694
- Fulvio Mora, Ideali di definizione e morfismi di schemi henseliani, Ann. Mat. Pura Appl. (4) 105 (1975), 191–204 (Italian, with English summary). MR 441959, DOI 10.1007/BF02414929
- Michel Raynaud, Anneaux locaux henséliens, Lecture Notes in Mathematics, Vol. 169, Springer-Verlag, Berlin-New York, 1970 (French). MR 0277519
- Marko Roczen, Henselsche Äquivalenz von Singularitäten, Wiss. Beitr. Martin-Luther-Univ. Halle-Wittenberg M 6 Beitr. Algebra Geom. 4 (1975), 29–46 (German). MR 0450277
- Oscar Zariski, Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields, Mem. Amer. Math. Soc. 5 (1951), 90. MR 41487
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 268 (1981), 445-465
- MSC: Primary 14A20; Secondary 13J15
- DOI: https://doi.org/10.1090/S0002-9947-1981-0632537-7
- MathSciNet review: 632537