Popescu Dorin-Mihail


Institute of Mathematics of the Romanian Academy
P.O. Box 1-764, RO-70700 Bucharest, Romania
phone: (401) 650 05 92
fax: (401) 222 98 26



Research interest

Scientific awards

Additional information

Scientifical Research

The main result of D. Popescu is the so called General Néron Desingularization which says that a morphism of Noetherian rings is regular iff it is a filtered inductive limit of smooth finite type algebras (see [27], [28], [39]). This result has the following two consequences:
  1. An excellent Henselian local ring has the Artin approximation property (in brief AP) [28].
  2. A regular local ring containing a field is a filtered inductive limit of regular local rings essentially of finite type over Z [34].
1. is a positive answer of a conjecture of M. Artin and it gives in particular the approximation on nested subrings which was required by mathematicians working in singularity theory [28].
2. is a partial answer to a conjecture of Swan and proves the Bass-Quillen conjecture in the equal characteristic case (that is a finitely generated projective module of a polynomial ring over a regular local ring containing a field is free [34]) using the Lindel's results.
Another result of D. Popescu (with G. Pfister) says that every noetherian local ring, which has AP has also the strong approximation property (see [12]). A very easy proof applying the General Néron Desingularization is given in [28].
Other results of D. Popescu are in the theory of maximal Cohen-Macaulay modules (in brief MCM). Some of them show the Brauer-Thrall Conjectures for MCM in some cases of unequalcharacteristic [38], [40], [41]. Others extend Knörrer's Periodicity Theorem in characteristic 2 (with Pfister) [46], or give an algorithm to describe the MCM modules over a singularity of type f(X)+Y_1^{s_1}+...+Y_r^{s_r} if you know the MCM modules over f (see some joint papers [47], [48], [51]-[53], [55]-[57]).
Recently D. Popescu has some results in Combinatorics in Commutative Algebra. Together with J. Herzog an extension of Green's theorem concerning the Hilbert functions is proved. As a consequence it shows some partial positive answers to some conjectures of Eisenbud-Green-Harris in the Cayley-Bacharach theory and the Higher Castelnuovo Theory ([50], [54]). Also the Betti numbers of some monomial ideals (p-stable) are computed [58] and it is shown that the Pardue conjecture holds in such cases.

List of publications

dorin@stoilow.imar.ro, dpopescu@gta.unibuc.ro