Conferència de Liam O'Carroll, Maxwell Institute of Mathematics, University of Edinburgh
(Joint work with S. Goto and F. Planas-Vilanova)

"J. Sally's Question and a Conjecture of Y. Shimoda"

Sala de juntes de l'FME, dimarts 4 d'octubre a les 15:00.

ABSTRACT
In 2007, Y. Shimoda, in connection with an open question of J. Sally from 1978,
conjectured that a Noetherian local ring, such that all its prime ideals different from the
maximal ideal are complete intersections, has Krull dimension at most two. This talk
surveys the results that have been obtained to date concerning this conjecture.
First we indicate that we can reduce to the case of dimension three, and that the
conjecture has a positive answer if the ring is either regular, or is complete with infinite
residue field and multiplicity at most three.
Finally we consider the case of the appropriate analogue of the conjecture for standard
graded rings, and indicate how a mix of algebraic and geometrical methods yields a
definite answer in this setting.