To every object of a symmetric tensor category over a field of characteristic we attach -adic integers Dim and Dim whose reduction modulo is the categorical dimension dim of , coinciding with the usual dimension when is a vector space. We study properties of Dim, and in particular show that they don't always coincide with each other, and can take any value in . We also discuss the connection of -adic dimensions with the theory of -rings and Brauer characters.
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Pavel Etingof, Nate Harman, Victor Ostrik, -adic dimensions in symmetric tensor categories in characteristic . Quantum Topol. 9 (2018), no. 1, pp. 119–140DOI 10.4171/QT/104