  We define the class of rigid Frobenius algebras in a (non-semisimple) modular
category and prove that their categories of local modules are, again, modular.
This generalizes previous work of A. Kirillov, Jr. and V. Ostrik [Adv. Math.
171 (2002), no. 2] in the semisimple setup. Examples of non-semisimple modular
categories via local modules, as well as connections to the authors' prior work
on relative monoidal centers, are provided. In particular, we classify rigid
Frobenius algebras in Drinfeld centers of module categories over group
algebras, thus generalizing the classification by A. Davydov [J. Algebra 323
(2010), no. 5] to arbitrary characteristic.
