$\mathscr{L}$invariants of Artin motives
Abstract
We compute Benois $\mathscr{L}$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 parametrized by a flag variety and thus depend on continuous parameters. We are nevertheless able to show in some examples, how Hida theory and the geometry of the eigencurve can be used to detect a finite number of choices of arithmetic and ``mixedmotivic'' significance.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.09719
 Bibcode:
 2022arXiv220509719D
 Keywords:

 Mathematics  Number Theory;
 11R23;
 11F80;
 11F33