English

Invariant dimensions and maximality of geometric monodromy action

Number Theory 2015-09-01 v1

Abstract

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

Keywords

Cite

@article{arxiv.1508.07499,
  title  = {Invariant dimensions and maximality of geometric monodromy action},
  author = {Chun Yin Hui},
  journal= {arXiv preprint arXiv:1508.07499},
  year   = {2015}
}