论文标题
$ \ Mathscr {l} $ - Artin动机不变
$\mathscr{L}$-invariants of Artin motives
论文作者
论文摘要
我们计算Benois $ \ Mathscr {l} $ - 重量$ 1 $ cuspforms及其伴随表示形式，并显示这如何扩展Gross'Gross'Gross'Udigne'$ p $ - addic调节器到Artin动机，这在Deligne的感觉上并不重要。 Benois的构造取决于选择常规的子模块，当表示为$ p $时，这是可以很好地理解的，因为这等于选择``动机''$ p $ forfinement。在$ p $的情况下，情况在情况下大不相同，在$ p $ irrenformular的情况下，普通的子模型由标志品种参数化，因此取决于连续参数。然而，我们仍然能够在一些示例中展示HIDA理论和特征库的几何形状如何用于检测有限数量的算术选择和``混合动力''的意义。
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 ``mixed-motivic'' significance.
