Reg ouvert et complexe cotangent. (Open reg and the cotangent complex) (Q1104990)

A noetherian ring A satisfies J-2 if for each A-algebra B essentially of finite type (equivalently for each A-algebra of finite type) Reg\((B)=\{Q\in \)Spec\((B);\) \(B_ Q\) is regular\} is open in Spec(B). Let \(d_ n(A_ P)=rank(H_ n(A,K,K))\) where \(K=A_ P/PA_ P\). A. Ragusa has proved that for excellent rings there are integers \(e_ k\) so that \(d_ k(A_ P)\leq\) \(e_ k\) for each P and each \(k\geq 2\) and even for \(k=1\) if \(\dim (A)<\infty\). This is generalized by the author to rings satisfying J-2. Furthermore it is shown that if A is of finite dimension and satisfies J-2, then \(H_ k(A,\prod A,\prod K_ i)=0\) for \(k\geq 0\) for each denumerable set of primes \(P_ i\) \((\prod A\) is the product of a denumerable set of copies of A, \(K_ i=A_{P_ i}/P_ iA_{P_ i})\). Conversely, if \(H_ 1(A,\prod A,\prod K_ i)=0\) for each denumerable set of primes, then A satisfies J-2.