On the rigidity of the cotangent complex at the prime 2 (Q1013097)

Let \(R \to A\) be a homomorphism of commutative noetherian rings. The yet unproven part of Quillen's Conjecture asserts that if the flat dimension of the cotangent complex \({\mathbf L}_{A/R}\) is finite, then that dimension is in fact less than or equal to 2. The main result of the paper shows that the conjecture is true when \(R\) is a Cohen--Macaulay ring of characteristic 2. The assumption on the characteristic allows the author to analyze the properties of the homotopy and homology of simplicial commutative algebras using Dwyer's higher divided squares.