Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Conditions for the existence of contractions in the category of algebraic spaces
HTML articles powered by AMS MathViewer

by Joseph Mazur PDF
Trans. Amer. Math. Soc. 209 (1975), 259-265 Request permission


Artin’s conditions for the existence of a new contraction of an algebraic subspace are changed. The new conditions are more applicable in special cases, especially when the subspace has a conormal bundle.
  • M. Artin, Algebraization of formal moduli. II. Existence of modifications, Ann. of Math. (2) 91 (1970), 88–135. MR 260747, DOI 10.2307/1970602
  • M. Artin, The implicit function theorem in algebraic geometry, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 13–34. MR 0262237
  • —, Algebraic spaces, Whittemore Lectures, Yale University, 1969 (mimeographed notes). N. Bourbaki, Éléments de mathématiques. Fasc. XXVIII. Algèbre commutative. Chap. 3: Graduations, filtrations et topoligies, Actualités Sci. Indust., no. 1293, Hermann, Paris, 1961. MR 30 #2027. J. Dieudonné and A. Grothendieck, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. Nos. 8, 11 (1960/61). MR 36 #177b, c.
  • Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
  • Robin Hartshorne, Ample vector bundles, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 63–94. MR 193092
  • Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977, DOI 10.1007/BFb0067839
  • Donald Knutson, Algebraic spaces, Lecture Notes in Mathematics, Vol. 203, Springer-Verlag, Berlin-New York, 1971. MR 0302647, DOI 10.1007/BFb0059750
  • J. Mazur, A relative étale topology for imbedded subschemes (to appear).
  • Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 68874, DOI 10.2307/1969915
  • O. Zariski, Algebraic surfaces, Springer, Berlin, 1935.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 14E15, 14A20
  • Retrieve articles in all journals with MSC: 14E15, 14A20
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 259-265
  • MSC: Primary 14E15; Secondary 14A20
  • DOI:
  • MathSciNet review: 0387280