On Simplicial Commutative Algebras with Vanishing André -quillen Homology

@inproceedings{Turner2000OnSC,
  title={On Simplicial Commutative Algebras with Vanishing Andr{\'e} -quillen Homology},
  author={James M. Turner},
  year={2000}
}
In this paper, we study the André-Quillen homology of simplicial commutative l-algebras, l a field, having certain vanishing properties. When l has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen… CONTINUE READING

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Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 16 references

Homologie des algèbres commutatives

  • M. André
  • Die Grundlehren der Mathematischen Wissenschaften…
  • 1974
Highly Influential
12 Excerpts

Cohomologie modulo 2 des espaces d’Eilenberg-MacLane

  • J.-P. Serre
  • Comment. Math. Helv. 27 (1953), 198-231
  • 1953
Highly Influential
5 Excerpts

Commutative ring theory, Cambridge Studies

  • H. Matsumura
  • Advanced Math
  • 1996

On the André-Quillen cohomology of commutative F2-algebras, Astérique

  • P. Goerss
  • 1990
3 Excerpts

A Hilton-Milnor theorem for categories of simplicial algebras

  • Amer. J. Math,. 111 (1989), 927–971.
  • 1989
2 Excerpts

On the non-vanishing of cotangent cohomology

  • L. Avramov, S. Halperin
  • Comment. Math. Helv. 62 (1987), 169-184.
  • 1987
1 Excerpt

The Sullivan conjecture on maps from classifying spaces

  • H. Miller
  • Annals of Math. 120 (1984), 39–87.
  • 1984
2 Excerpts

Homology of symmetric algebras

  • M.-A. Nicollerat
  • Commun. Algebra 7 (1978), 657-676
  • 1978
1 Excerpt

On the (co)homology of commutative rings

  • Proc. Symp. Pure Math. 17(1970), 65–87.
  • 1970
3 Excerpts

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