# $\mathscr{L}$-invariants of Artin motives

@inproceedings{Dimitrov2022mathscrLinvariantsOA, title={\$\mathscr\{L\}\$-invariants of Artin motives}, author={Mladen Dimitrov and Alexandre Maksoud}, year={2022} }

. We compute Benois L -invariants of weight 1 cuspforms and of their adjoint representations and show how this extends Gross’ p -adic regulator to Artin motives which are not critical in the sense of Deligne. Benois’ construction depends on the choice of a regular submodule which is well understood when the representation is p -regular, as it then amounts to the choice of a “motivic” p -reﬁnement. The situation is dramatically diﬀerent in the p -irregular case, where the regular submodules are…

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