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arXiv · 2401.02350

Locally dualizable modules abound

Jon F. Carlson·Srikanth B. Iyengar
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Abstract

It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3.

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Jon F. Carlson, Srikanth B. Iyengar. 2024-01-04. Locally dualizable modules abound. https://arxiv.org/abs/2401.02350

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