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Le groupe de Witt d'une surface réelle

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Commentarii Mathematici Helvetici

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Bibliographie

  1. R. Baeza,Quadratic forms over semi local rings, Springer Lecture Notes in Math. 655 (1978).

  2. H. Bass,Algebraic K-theory, Benjamin, New York (1968).

    MATH  Google Scholar 

  3. H. Bass,Clifford algebras and spinor norms over a commutative ring, Amer. J. of Math.96 (1974) pp. 156–206.

    Article  MathSciNet  Google Scholar 

  4. N. Bourbaki,Algèbre commutative, chap. 1–7, Hermann, Paris (1967).

    Google Scholar 

  5. J.-L. Colliot-Thélène etJ.-J. Sansuc,Cohomology of groups of multiplicative type over regular schemes, C.R. Acad. Sci. Paris 287, Series A et B, no. 6 (1978).

  6. C. W. Curtis andI. Reiner,Representation theory of finite groups and associative algebras, Intersciences (1962).

  7. G. Dietel, Wittringe reeller Kurven, Thesis, Regensburg (1981).

  8. R. Elman andT. Y. Lam,Quadratic forms over formally real fields and Pythagorean fields, Am. J. of Math.94 (1972), 1155–1194.

    Article  MathSciNet  Google Scholar 

  9. R. Elman andT. Y. Lam,Classification Theorems for Quadratic forms over field, Comm. Math. Helv.49 (1974), 373–381.

    MathSciNet  Google Scholar 

  10. R. M. Fossum,The divisor class group of a Krull domain, Ergebnisse der Math. und ihrer Grenzgebiete, Band 74, Springer, Berlin-Heidelberg-New York (1973).

    MATH  Google Scholar 

  11. A. Grothendieck,Le groupe de Brauer I, II, III, in Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam (1968), pp. 46–188.

    Google Scholar 

  12. A. Grothendick etJ. Dieudonné, EGA 4. Etude locale des schémas et des morphismes de schémas, Publ. math. I.H.E.S. (1964–1967).

  13. R. Hartshorne,Algebraic geometry, Graduate texts in Math. 52, Springer New York-Heidelberg-Berlin (1977).

    MATH  Google Scholar 

  14. P. J. Hilton andU. Stammbach,A course in homological algebra, Springer, New York-Heidelberg-Berlin (1970).

    Google Scholar 

  15. H. Hironaka,Resolution of singularities of an algebraic variety over a field of characteristic zero, Annals of Math.79 (1964), 109–326.

    Article  MathSciNet  Google Scholar 

  16. H. Hironaka,Formal Line Bundles along Exceptional Loci, InAlgebraic Geometry, Bombay Colloquium 1968, Bombay (1969).

  17. M. Knebusch,Symmetric bilinear forms over algebraic varieties, Queen's Papers in Pure and App. Math46 (1977), 103–283.

    MathSciNet  Google Scholar 

  18. M. Knebusch,On algebraic curves over real closed fields II, Math. Z.151 (1976), 189–205.

    Article  MathSciNet  Google Scholar 

  19. T. Y. Lam,The algebraic theory of Quadratic forms, Benjamin (1973).

  20. J. S. Milne,Etale Cohomology, Princeton Univ. Press (1980).

  21. J. Mulnor,Introduction to Algebraic K-theory, Ann, of Math. Studies 72, Princeton Univ. Press (1970).

  22. M. Ojanguren,A splitting theorem for quadratic forms, Comm. Math. Helv.57 (1982), 145–157.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. R. Parimala andR. Sridharan, Quadratic forms over rings of dimension 1, Comm. Math. Helv. (1980), 634–644.

  25. H. G. Quebbemann, W. Scharlau andM. Schulte,Quadratic and Hermitian Forms in additive and abelian categories, J. of Alg. 59, (1979), 264–289.

    Article  MathSciNet  Google Scholar 

  26. M. Raynaud,Anneaux locaux henséliens, Springer Lecture Notes in Math.169 (1970).

  27. A. Roy,Cancellation of quadratic forms over commutative rings, J. of Alg.10 (1968), 286–298.

    Article  Google Scholar 

  28. P. Samuel,A propos du théorème des unités, Bull. Sci. Math.90 (1966), 89–96.

    MathSciNet  Google Scholar 

  29. Séminaire de géométrie algébrique SGA 2: Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz, North-Holland, Amsterdam (1968), pp. 124–135.

  30. Séminaire de géométrie algébrique du Bois Marie 1963–64, SGA 4: Théorie des topos et cohomologie étale des schémas, tome 3, Springer Lecture Notes in Math. 305 (1973), pp. 206–249.

  31. J.-R. Serre,Géométrie algébrique et géométrie analytique, Annales de l'Institut Fourier6 (1955), 1–42.

    MathSciNet  Google Scholar 

  32. R. G. Swan,K-theory of finite groups and orders, Springer Lecture Notes in Math. 149 (1970).

  33. V. S. Varadarajan,Lie groups, Lie algebras, and their representations, Prentice Hall, Serie in modern analysis (1974).

  34. L. N. Vaserstein,Stabilization of Unitary and orthogonal groups over a ring with involution. Math. Sbornik81 (1970), 307–326.

    Article  MathSciNet  Google Scholar 

  35. C. Weibel,Complete intersection points of affine surfaces, Preprint.

  36. A. Weil,Courbes algébriques et variétés abéliennes, Hermann, Paris (1971).

    MATH  Google Scholar 

  37. O. Zariski andP. Samuel,Commutative algebra (Vol. I, II), Van Nostrand, Princeton (1958, 1960).

    MATH  Google Scholar 

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Ayoub, G. Le groupe de Witt d'une surface réelle. Commentarii Mathematici Helvetici 62, 74–105 (1987). https://doi.org/10.1007/BF02564439

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