Mittag-Leffler conditions on modules

Details Mittag-Leffler conditions on modules Mittag-Leffler conditions on modules

2007-04-27

arxiv.org/abs/0704.3690v1

Mathematics

Rings and Algebras

45 pages

Scientific paper

We study Mittag-Leffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting problem. Moreover, we show that modules arising in cotorsion pairs satisfy certain Mittag-Leffler conditions. In particular, this implies that tilting modules satisfy a useful finiteness condition over their endomorphism ring. In the final section, we focus on a special tilting cotorsion pair related to the pure-semisimplicity conjecture.

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