Monodromy filtration and motives

Abhijit Laskar (1)

1 IRMA - Institut de Recherche Mathématique Avancée

For a given number field $F$ and a non-archimedean valuation on $F$, we establish the existence of weight filtration on the $\ell$-adic realizations of any pure motive $M$ defined over $F$. Using this filtration we state a motivic analogue of the Weight monodromy conjecture of Deligne. We prove this conjecture in special cases and from this we deduce some new instances of the original Weight monodromy conjecture of Deligne.

Mots clés: motives; weight monodromy conjecture

Domaines: Théorie des nombres [math.NT]

Abhijit Laskar. Monodromy filtration and motives. 2014. ⟨hal-01068065v1⟩