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Algebraic K-theory of the integers

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Higher Algebraic K-Theory: an overview

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References

  1. Adams, J.F.: On the groups J(X) — III. Topology 3 (1965) 193–222

    Article  MathSciNet  MATH  Google Scholar 

  2. Arlettaz, D.: Chern-Klassen von ganzzahligen und rationalen Darstellungen diskreter Gruppen. Math. Zeits. bf 187 (1984) 49–60

    Article  MathSciNet  MATH  Google Scholar 

  3. Ash, A.: Small-dimensional classifying spaces for arithmetic subgroups of general linear groups. Duke Math. J. 51, No. 2 (1984) 459–468

    Article  MathSciNet  MATH  Google Scholar 

  4. Bass, H., Tate, J.: The Milnor ring of a global field. In: Algebraic K-Theory II. Lecture Notes in Maths. No. 342 (1973) 349–446. Springer-Verlag

    Google Scholar 

  5. Beilinson, A.: Higher regulators and values of L-functions. Journal Soviet Mathematics 30 (1985) 2036–2070

    Article  MATH  Google Scholar 

  6. Bloch, S.: Lectures on algebraic cycles. Duke University Mathematics series 4 (1980)

    Google Scholar 

  7. Borel, A.: Introduction aux groupes arithmétiques (1965) Hermann ed.

    Google Scholar 

  8. Borel, A.: Stable real cohomology of arithmetic groups. Ann. Scient. Ec. Norm. Sup. 4ème série, t. 7 (1974) 235–272

    MathSciNet  MATH  Google Scholar 

  9. Borel, A.: Cohomologie de S L n et valeurs de fonctions zêta. Ann. Sci. Scuola Norm. Sup. Pisa 4 (1977) 613–636

    MathSciNet  MATH  Google Scholar 

  10. Borel, A., Serre, J.P.: Corners and arithmetic groups. Comm. Math. Helv. 48 (1974) 244–297

    MathSciNet  Google Scholar 

  11. Borevich, I.I., Shafarevich, I.R.: Number Theory. Academic Press, 1966

    Google Scholar 

  12. Bott, R.: The stable homotopy of the classical groups. Annals of Maths. Vol. 70, No. 2 (1959) 313–337

    Article  MathSciNet  MATH  Google Scholar 

  13. Browder, W.: Algebraic K-theory with coefficients ℤ/p. Lecture Notes in Math. No. 657 (1978), 40–85. Springer-Verlag

    Google Scholar 

  14. Cartan, H., Eilenberg, S.: Homological Algebra. Princeton University Press, 1956

    Google Scholar 

  15. Coates, J., Lichtenbaum, S.: On ℓ-adic zeta functions. Annals of Maths. 98, No. 3 (1973) 498–550

    Article  MathSciNet  MATH  Google Scholar 

  16. Dwyer, W., Friedlander, E.: Algebraic and etale K-theory, Trans. Amer. Math. Soc. 272 (1985) 247–280

    MathSciNet  MATH  Google Scholar 

  17. Eckmann, B., Mislin, G.: Chern classes of group representations over a number field. Compositio Math. 44 (1981) 41–65

    MathSciNet  MATH  Google Scholar 

  18. Evens, L., Kahn, D.S.: Chern classes of certain representations of symmetric groups. Trans. AMS 245 (1978) 309–330

    Article  MathSciNet  MATH  Google Scholar 

  19. Gabber, O.: K-Theory of henselian pairs, preprint (1984)

    Google Scholar 

  20. Gillet, H., Thomason, R.: The K-theory of strict Hensel local rings and a theorem of Suslin. Journal of pure and appl. Algebra 34 (1984) 241–254

    Article  MathSciNet  MATH  Google Scholar 

  21. Grothendieck, A.: Classes de Chern des représentations de groupes discrets. In: Dix exposés sur la cohomologie des schémas. North-Holland, Masson, 1968

    Google Scholar 

  22. Iwasawa, K.: Lectures on p-adic L-functions. Annals of Math. Studies 74 (1972), Princeton University Press

    Google Scholar 

  23. Lee, R., Szczarba, R.H.: The group K 3(ℤ) is cyclic of order 48. Annals of Math. 104 (1976), 31–60

    Article  MathSciNet  MATH  Google Scholar 

  24. Lee, R., Szczarba, R.H.: On the torsion in K 4(ℤ) and K 5(ℤ). Duke Math. Journal 45 No. 1 (1978) 101–130, with an Addendum by Soulé, C., p. 131–132

    Article  MathSciNet  Google Scholar 

  25. Levine, M.: The indecomposable K 3 of fields. Ann. Ec. Norm. Sup. 22 (1989) 255–344

    MathSciNet  MATH  Google Scholar 

  26. Lichtenbaum, S.: Values of zeta functions, étale cohomology, and algebraic K-theory. In: Algebraic K-Theory II. Lecture Notes in Maths. No. 342 (1973) 489–501. Springer-Verlag

    Google Scholar 

  27. Loday, J.L.: K-Théorie algébrique et représentations de groupes. Ann. Sci. Ec. Norm. Sup., Série 4, 9 (1976) 309–377

    MathSciNet  MATH  Google Scholar 

  28. Mazur, B., Wiles, A.: Class fields of abelian extensions of ℚ. Invent. Math. 76 (1984) 179–330

    Article  MathSciNet  MATH  Google Scholar 

  29. Merkurjev, A.S., Suslin, A.A.: K-cohomology of Severi-Brauer varieties and norm residue homomorphism. Izv. AN USSR, 46, No. 5 (1982) 1011–1046

    MathSciNet  Google Scholar 

  30. Merkurjev, A.S., Suslin, A.A.: On the K 3 of a field. Preprint LOMI (1987)

    Google Scholar 

  31. Milnor, J., Stasheff, J.: Characteristic classes. Annals of Maths. Studies 76 (1974) Princeton University Press

    Google Scholar 

  32. Milnor, J.: Introduction to algebraic K-theory. Annals of Maths. Studies 72 (1971) Princeton University Press

    Google Scholar 

  33. Minkowski, H.: Diskontinuitätsbereich für arithmetische Äquivalenz. Gesammelte Abhandlungen 2 (1905) 53–100

    Google Scholar 

  34. Quillen, D.: Higher Algebraic K-Theory. International Congress of Mathematicians, Vancouver (1974) 171–176

    Google Scholar 

  35. Quillen, D.: Higher algebraic K-theory I. In: Algebraic K-Theory I. Lecture Notes in Maths. No. 341 (1973) 85–147. Springer-Verlag

    Google Scholar 

  36. Quillen, D.: Finite generation of the groups K i of algebraic integers. In: Algebraic K-Theory I. Lecture Notes in Maths. No. 341 (1973) 178–198. Springer-Verlag

    Google Scholar 

  37. Quillen, D.: Letter to Milnor, July 26, 1972. In: Lecture Notes in Mathematics No. 551 (1976) 182–188

    Google Scholar 

  38. Serre, J.P.: Arbres, amalgames, SL 2. Astérisque 46 (1977)

    Google Scholar 

  39. Soulé, C.: The cohomology of SL 3(ℤ). Topology 17 (1978) 1–22

    Article  MathSciNet  Google Scholar 

  40. Soulé, C.: Groupes arithmétiques et K-théorie des anneaux d'entiers de corps de nombres. Thèse d'état (1978) Université de Paris VII

    Google Scholar 

  41. Soulé, C.: K-Théorie des anneaux d'entiers de corps de nombres et cohomologie étale. Invent. Math. 55 (1979) 251–295

    Article  MathSciNet  MATH  Google Scholar 

  42. Soulé, C.: Classes de torsion dans la cohomologie des groupes arithmétiques. C.R. Acad. des Sc. Paris 284 (1977) 1009–1011

    MATH  Google Scholar 

  43. Soulé, C.: Groupes de Chow et K-théorie de variétés sur un corps fini. Math. Ann. 268 (1984) 317–345

    Article  MathSciNet  MATH  Google Scholar 

  44. Soulé, C.: K-Théorie et zéros aux points entiers de fonctions zêtas. International congress of Mathematicians, Warsaw (1983) 437–445

    Google Scholar 

  45. Staffeldt, R.E.: Reduction theory and K 3 of the Gaussian integers. Duke Math. Journal 45, No. 4 (1979) 773–791

    Article  MathSciNet  MATH  Google Scholar 

  46. Suslin, A.A.: Stability in algebraic K-theory. Lecture Notes in Math. No. 966 (1982) 344–356

    Google Scholar 

  47. Suslin, A.A.: On the K-theory of algebraically closed fields. Invent. Math. 73 (1983) 241–245

    Article  MathSciNet  MATH  Google Scholar 

  48. Suslin, A.A.: On the K-theory of local fields. J. of pure and appl. algebra 34 (1984) 301–318

    Article  MathSciNet  MATH  Google Scholar 

  49. Tate, J.: Relations between K 2 and Galois cohomology. Invent. Math. 36 (1976) 257–274

    Article  MathSciNet  MATH  Google Scholar 

  50. Thomason, R.W.: Algebraic K-theory and étale cohomology. Ann. Sc. Ec. Norm. Sup. 18, No. 3 (1985) 437–552

    MathSciNet  MATH  Google Scholar 

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  1. Institut des Hautes Études Scientifiques, 35, Route de Chartres, F-91440, Bures-sur-Yvette

    Christophe Soulé

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  1. Christophe Soulé
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Soulé, C. (1992). Algebraic K-theory of the integers. In: Higher Algebraic K-Theory: an overview. Lecture Notes in Mathematics, vol 1491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088880

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  • DOI: https://doi.org/10.1007/BFb0088880

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