Graded algebra of a valuation
by
Olivier Piltant
CNRS and Ecole Polytechnique - Palaiseau - France

In algebraic geometry and singularity theory, valuation rings often appear as overrings of a "well behaved" ring R (e.g. a ring of germs of algebraic functions at a point of an algebraic variety). The ring R inherits a filtration by valuation ideals.

My talk will be focused on the following problem: what can be said about the graded algebra of R with respect to the above filtration? The main questions addressed will be about its Krull dimension, Hilbert function, and finiteness.

Date received: May 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-47.