FROBENIUS POWERS OF COMPLETE INTERSECTIONS
LUCHEZAR L. AVRAMOV AND CLAUDIA MILLER
Let R be a commutative noetherian local ring of characteristic p > 0, and let
OE: R ! R be the Frobenius endomorphism, OE(a)r= ap. Each iterationrOEr defines
on R a new structure of R-module, denoted OER, for which a . b =rap b.
In 1969 Kunz [7, (3.3)] observedrthat if R is regular, then OER is flat for a*
*ll r 0
and he discovered that if OER is flat for some r 1, then R is regular. Regula*