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ANDRE-QUILLEN HOMOLOGY OF ALGEBRA RETRACTS LUCHEZAR L. AVRAMOV AND SRIKANTH IYENGAR
 

Summary: ANDRŽE-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 AndrŽe-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 = idS. More precisely, in this case we show that
is complete intersection at -1
(n) for every prime ideal n of S. Using these results,
we describe all algebra retracts S R S for which the algebra TorR
· (S, S) is
finitely generated over TorR
0 (S, S) = S.
HOMOLOGIE D'ANDRŽE-QUILLEN DES ALG`EBRES SCINDŽEES
ResumŽe. ŽEtant donnŽe un homomorphisme : R S d'anneaux commutatifs
noethŽeriens, Daniel Quillen a conjecturŽe en 1970 que si les foncteurs Dn(S|R; -)
d'homologie d'AndrŽe-Quillen sont nuls pour tout n 0, alors ils sont nuls pour
tout n 3. Nous dŽemontrons cette conjecture sous l'hypoth`ese supplŽementaire
qu'il existe un homomorphisme d'anneaux : S R tel que = idS. Plus
prŽecisemment, nous montrons que dans ce cas est d'intersection compl`ete en

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics