Coartinianness of extension and torsion functors.

Let (R , m) be a commutative noetherian local ring with m -adic topology, I an ideal of R. We investigate coartinianness of Ext and Tor , show that the R-module Ext R i (N , M) is I-coartinian if M is a linearly compact I-coartinian R-module and N is an I-cofinite R-module of dimension at most 1; the R-module Tor i R (N , M) is I-coartinian in the case M is semi-discrete linearly compact I-coartinian and N is finitely generated with dimension at most 2. [ABSTRACT FROM AUTHOR]