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Summary:
ANDR'E-QUILLEN HOMOLOGY OF ALGEBRA RETRACTS
LUCHEZAR L. AVRAMOV AND SRIKANTH IYENGAR
Abstract. Given a homomorphism of commutative noetherian rings ': R ! S,
Daniel Quillen conjectured in 1970 that if the Andr'e-Quillen homology functors
Dn(S|R; -) vanish for all n 0, then they vanish for all n 3. We prove the
conjecture under the additional hypothesis that there exists a homomorphism of
rings _ :S ! R such that ' O _ = idS. More precisely, in this case we show that*
* _
is complete intersection at '-1(n) for every prime ideal n of S. Using these re*
*sults,
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