MONODROMY FILTRATION AND MOTIVES

Abhijit Laskar (1)

1 VU - Vrije Universiteit Amsterdam [Amsterdam]

Given a (pure) motive M over a number field F and a non-archimedean valuation v on F , we state an analogue of the weight monodromy conjecture for M , via a local weight filtration W • on the-adic realization H (M). We prove special cases of this conjecture. In some of these cases, we are able to show that the local L-factor at v, of the L-function of M , is well-defined i.e., rational and independent of .

Mots clés: motives; weight monodromy conjecture

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Abhijit Laskar. MONODROMY FILTRATION AND MOTIVES. 2014. ⟨hal-01068065v2⟩