This is an announcement for the paper "On dominated polynomials between Banach spaces" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this paper, among other results, we prove a conjecture concerning coincidence theorems for dominated polynomials. We also obtain an abstract version of Pietsch Domination Theorem (PDT) which unifies and generalizes several different nonlinear approaches; our result recovers, as a particular case, the well-known PDT for dominated multilinear mappings. Archive classification: math.FA Mathematics Subject Classification: 46B15; 46G25 Remarks: 10 pages The source file(s), conjecture19agosto2008-arxiv.tex: 34210 bytes, is(are) stored in gzipped form as 0809.4496.gz with size 10kb. The corresponding postcript file has gzipped size 85kb. Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4496 or http://arXiv.org/abs/0809.4496 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4496 or in gzipped form by using subject line get 0809.4496 to: math@arXiv.org.