On Simplicial Commutative Algebras with Finite André-quillen Homology
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چکیده
In [22, 4] a conjecture was posed to the effect that if R → A is a homomorphism of Noetherian rings then the André-Quillen homology on the category of A-modules satisfies: Ds(A|R;−) = 0 for s ≫ 0 implies Ds(A|R;−) = 0 for s ≥ 3. In [28], an extended version of this conjecture was considered for which A is a simplicial commutative R-algebra with Noetherian homotopy such that char(π0A) 6= 0. In addition, a homotopy characterization of such algebras was described. The main goal of this paper is to develop a strategy for establishing this extended conjecture and provide a complete proof when R is Cohen-Macaulay of characteristic 2.
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تاریخ انتشار 2008