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Picard schemes of formal schemes; application to rings with discrete divisor class group

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Classification of Algebraic Varieties and Compact Complex Manifolds

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 412))

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References

  1. A. GROTHENDIECK, J. DIEUDONNÉ, Éléments de Géométrie Algébrique: Springer-Verlag, Heidelberg, 1971.

    MATH  Google Scholar 

  2. I, II, III(0III), IV(0IV), Publ. Math. I.H.E.S. 4,8,...

    Google Scholar 

  3. A. GROTHENDIECK et. al., Séminaire de Géométrie Algébrique: Cohomologie locale des faisceaux cohérents..., North-Holland, Amsterdam, 1968.

    MATH  Google Scholar 

  4. A. GROTHENDIECK et. al., Séminaire de Géométrie Algébrique: Schémas en groupes I, Lecture Notes in Mathematics no. 151, Springer-Verlag, Heidelberg, 1970.

    MATH  Google Scholar 

  5. A. GROTHENDIECK et. al., Séminaire de Géométrie Algébrique: Théorie des intersections et théorème de Riemann-Roch, Lecture Notes in Mathematics no. 225, Springer-Verlag, Heidelberg, 1971.

    Google Scholar 

  6. N. BOURBAKI, Algèbre Commutative, Hermann, Paris. (English Translation, 1972).

    MATH  Google Scholar 

  7. J.-F. BOUTOT, Schéma de Picard local, C. R. Acad. Sc. Paris, 277 (Série A) (1973), 691–694.

    MathSciNet  MATH  Google Scholar 

  8. V. I. DANILOV, On a conjecture of Samuel, Math. USSR Sb. 10 (1970), 127–137. (Mat. Sb. 81 (123) (1970), 132–144.)

    Article  MATH  Google Scholar 

  9. _____, Rings with a discrete group of divisor classes, Math. USSR Sb. 12 (1970), 368–386. (Mat. Sb. 83 (125) (1970), 372–389.)

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, On rings with a discrete divisior class group, Math. USSR Sb. 17 (1972), 228–236. (Mat. Sb. 88 (130) (1972), 229–237.)

    Article  Google Scholar 

  11. M. DEMAZURE, P. GABRIEL, Groupes Algébriques (Tome I), North-Holland, Amsterdam, 1970.

    MATH  Google Scholar 

  12. R. M. FOSSUM, The divisor class group of a Krull domain, (Ergebnisse der Math., vol. 74), Springer-Verlag, Heidelberg, 1973.

    Book  MATH  Google Scholar 

  13. A. GROTHENDIECK, Groupe de Brauer III, in Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968.

    Google Scholar 

  14. W. KRULL, Beiträge zur Arithmetik kommutativer Integritätsbereiche V, Math. Z. 43 (1938), 768–782.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. LIPMAN, Rational Singularities ..., Publ. Math. I.H.E.S. no. 36 (1969), 195–279.

    Google Scholar 

  16. _____, The Picard group of a scheme over an Artin ring, to appear (preprint available).

    Google Scholar 

  17. D. PRILL, The divisor class groups of some rings of holomorphic functions, Math. Z. 121 (1971), 58–80.

    Article  MathSciNet  MATH  Google Scholar 

  18. P. SAMUEL, On unique factorization domains, Illinois J. Math. 5 (1961), 1–17.

    MathSciNet  MATH  Google Scholar 

  19. _____, Sur les anneaux factoriels, Bull. Soc. Math. France 89 (1961), 155–173.

    MathSciNet  MATH  Google Scholar 

  20. P. SALMON, Su un problema posto da P. Samuel, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 40 (1966), 801–803.

    MathSciNet  MATH  Google Scholar 

  21. G. SCHEJA, Einige Beispiele faktorieller lokaler Ringe, Math. Ann. 172 (1967), 124–134.

    Article  MathSciNet  MATH  Google Scholar 

  22. J.-P. SERRE, Corps locaux, Hermann, Paris, 1968.

    MATH  Google Scholar 

  23. U. STORCH, Über die Divisorenklassengruppen normaler komplexanalytischer Algebren, Math. Ann. 183 (1969), 93–104.

    Article  MathSciNet  MATH  Google Scholar 

  24. _____, Über das Verhalten der Divisorenklassengruppen normaler Algebren bei nicht-ausgearteten Erweiterungen, Habilitationsschrift, Univ. Bochum, (1971).

    Google Scholar 

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Authors
  1. Joseph Lipman
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Herbert Popp

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© 1974 Springer-Verlag

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Lipman, J. (1974). Picard schemes of formal schemes; application to rings with discrete divisor class group. In: Popp, H. (eds) Classification of Algebraic Varieties and Compact Complex Manifolds. Lecture Notes in Mathematics, vol 412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066156

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  • DOI: https://doi.org/10.1007/BFb0066156

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06951-5

  • Online ISBN: 978-3-540-37877-8

  • eBook Packages: Springer Book Archive

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