This is an announcement for the paper "Absolutely summing linear operators into spaces with no finite cotype" by Geraldo Botelho and Daniel Pellegrino. Abstract: Given an infinite-dimensional Banach space $X$ and a Banach space $Y$ with no finite cotype, we determine whether or not every continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing for almost all choices of $p$ and $q$, including the case $p=q$. If $X$ assumes its cotype, the problem is solved for all choices of $p$ and $q$. Applications to the theory of dominated multilinear mappings are also provided. Archive classification: math.FA Mathematics Subject Classification: 47B10 Remarks: 7 pages The source file(s), Botelho-Pellegrino-BullPolish.tex: 22261 bytes, is(are) stored in gzipped form as 0801.2051.gz with size 7kb. The corresponding postcript file has gzipped size 74kb. Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2051 or http://arXiv.org/abs/0801.2051 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2051 or in gzipped form by using subject line get 0801.2051 to: math@arXiv.org.