103 research outputs found
Mittag-Leffler conditions on modules
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.Comment: 45 page
Tilting and cotilting modules over concealed canonical algebras
We study infinite dimensional tilting modules over a concealed canonical
algebra of domestic or tubular type. In the domestic case, such tilting modules
are constructed by using the technique of universal localization, and they can
be interpreted in terms of Gabriel localizations of the corresponding category
of quasi-coherent sheaves over a noncommutative curve of genus zero. In the
tubular case, we have to distinguish between tilting modules of rational and
irrational slope. For rational slope the situation is analogous to the domestic
case. In contrast, for any irrational slope, there is just one tilting module
of that slope up to equivalence. We also provide a dual description of infinite
dimensional cotilting modules and a classification result for the
indecomposable pure-injective modules.Comment: 25 page
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