## Irrégularité et conducteur de Swan $p$-adiques

### Summary

Summary: Let $V$ be a de-Rham representation of the Galois group of a local field of mixed characteristic $(0,p)$. We relate the Swan conductor of the associated Weil-Deligne representation to the irregularity of the corresponding $p$-adic differential equation.

### Mathematics Subject Classification

11F80, 11F85, 11S15, 12H25

### Keywords/Phrases

$p$-adic representation, de-Rham representation, swan conductor, $p$-adic differential equation, $p$-adic irregularity