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This work is devoted to study of algebraicty modulo p of Siegel'sG-functions. Our goal is to emphasize the relevance of the notion of strongFrobenius structure, clasically studied in the theory of the p-adicdiffenrential equations, for the study of a Adamczewski-Delaygue's conjectureconcerning of the degree of algebraicity modulo p of G-functions. For this, wefirst make a Christol's result explicit by showing that if $f$ is a G-functionthat is solution of a differential operator $L$ in $ \mathbb{Q}(z)[d/dz]$ oforder $n$ endowed of a strong Frobenius structure of period $h$ for the primenumber $p$ and that $f(z)$ belongs to $\mathbb{Z}_{(p)}[[z]]$, then thereduction of $f$ modulo $ p $ is algebraic over $\mathbb F_p(z)$ and itsalgebraicity degree is bounded by $p^{n^2h}$. By generalizing an approachintroduced by Salinier, we show that if $L$ is a Fuchsian operator withcoefficients in $\mathbb{Q}(z)$, whose monodromy group is rigid and whoseexponents are rational numbers, then $L$ has for almost every prime number $p$a strong Frobenius structure of period $h$, where $h$ is explicitly bounded anddoes not depend on $p$. A slightly different version of this result has beenrecently demonstrated by Crew following a different approach based on the $p$-adic cohomology. We use these two results to solve the mentioned conjecture inthe case of generalized hypergeometric series.

Alg\'ebricit\'e modulo p, s\'eries hyperg\'eom\'etriques et structures de Frobenius forte