On a torsion analogue of the weight-monodromy conjecture

We formulate and study a torsion analogue of the weight-monodromy conjecture for proper smooth scheme over non-archimedean local field. prove it schemes equal characteristic fields, abelian varieties, surfaces, varieties uniformized by Drinfeld upper half spaces, set-theoretic complete intersections in toric varieties. In case, our methods rely on an ultraproduct variant Weil II established Cadoret.