Invariant dimensions and maximality of geometric monodromy action
Abstract
Let X be a smooth separated geometrically connected variety over Fq and f:Y-> X a smooth projective morphism. We compare the invariant dimensions of the l-adic representation Vl and the Fl-representation Vl of the geometric \'etale fundamental group of X arising from the sheaves Rwf*Ql and Rwf*Z/lZ respectively. These invariant dimension data is used to deduce a maximality result of the geometric monodromy action on Vl whenever Vl is semisimple and l is sufficiently large. We also provide examples for Vl to be semisimple for l>>0.
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