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Finite generation of K-groups of a curve over a finite field

After daniel quillen

Part I

Part of the Lecture Notes in Mathematics book series (LNM,volume 966)

Keywords

  • Vector Bundle
  • Simplicial Complex
  • Finite Field
  • Valuation Ring
  • Coordinate Ring

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References

  1. S. Bloch, Algebraic K-theory and Class field theory for Arithmetic Surfaces, preprint.

    Google Scholar 

  2. H. Bass, J. Milnor, J.-P. Serre, Solution of the Congruence Subgroup Problem for Sln (n ≥ 3) and Sp2n (n ≥ 2), I.H.E.S. Publ. Math. 33 (1967) 59–137.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. F. Bruhat and J. Tits, Groupes reductifs sur un corps local. I. Données radicielles valuées. Publ. Math. I.H.E.S. 41 (1972) 5–251.

    CrossRef  MathSciNet  Google Scholar 

  4. G. Harder, Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern, Inventiones Math. 42 (1977) 135–175.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. G. Harder, M.S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Annalen 212 (1975) 215–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. J. Milnor, The realizationof a semi-simplicial complex, Annals of Math. 65 (1957) 272–280.

    CrossRef  MathSciNet  Google Scholar 

  7. M.S. Narasimhan, C.S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Annals of Math. 82 (1965) 540–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. D. Quillen, Higher algebraic K-theory: I, in "Algebraic K-theory I", Lecture Notes in Math. #341, Springer-Verlag, Berlin (1973) 77–139.

    Google Scholar 

  9. D. Quillen, Finite generation of the groups Ki of rings of algebraic integers, same volume, 195–214.

    Google Scholar 

  10. D. Quillen, On the cohomology and K-theory of the general linear groups over a finite field, Annals of Math. 96 (1972) 552–586.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. D. Quillen, Homotopy properties of the poset of nontrivial p-subgroups of a group, Advances in Math., 28 (1978) 101–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. G. Segal, Classifying Spaces and Spectral Sequences, Publ. Math. I.H.E.S. 34 (1968) 105–112.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J.-P. Serre, Arbres, Amalgames, Sl2, Soc. Math. de France, Asterisque #46 (1977), Paris.

    Google Scholar 

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© 1982 Springer-Verlag

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Grayson, D.R. (1982). Finite generation of K-groups of a curve over a finite field. In: Dennis, R.K. (eds) Algebraic K-Theory. Lecture Notes in Mathematics, vol 966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062167

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  • DOI: https://doi.org/10.1007/BFb0062167

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11965-4

  • Online ISBN: 978-3-540-39553-9

  • eBook Packages: Springer Book Archive