  The Tate conjecture has two parts: i) Tate classes are linear combination of
algebraic classes, ii) semisimplicity of Galois representations (for smooth
projective varieties).
  B. Moonen proved that i) implies ii) in characteristic 0, using $p$-adic
Hodge theory.
  We show that an unconditional result lies behind this implication: the {\it
observability} of arithmetic monodromy groups of geometric origin (in any
characteristic) - which leads to a sharpening of Moonen's result.
  We also discuss another aspect of the Tate conjecture related to the
transcendence of $p$-adic periods.
