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

On the observability of Galois representations and the Tate conjecture