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On the André-Quillen Cohomology of commutative $\mathbb {F}_2$-algebras

On the André-Quillen Cohomology of commutative $\mathbb {F}_2$-algebras

Paul G. GOERSS
On the André-Quillen Cohomology of commutative $\mathbb {F}_2$-algebras
  • Année : 1990
  • Tome : 186
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 13D03
  • Nb. de pages : 184
  • ISSN : 0303-1179
  • DOI : 10.24033/ast.27

Quillen and André have rigorized and explored a notion of cohomology algebras or, more generally, simplicial commutative algebras. They were able to do a number of systematic calculations, especially when concerned with a local ring with resiude field of characteristic 0, but the case when the characteristic was non-zero remained a problem. However, for certain applications – for example, to homotopy theory – the non-zero characteristic case is vital. In this paper we explore André-Quillen cohomology of supplemented algebras avec the field $\mathbb {F}_2$ of two elements, and completely determine the structure of this cohomology, including a product and “Steenrod” operations. A necessary part of the program is a complete examination of the homotopy theory of simplicial algebras. For this we draw on the work of many authors.

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