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We prove Gieseker conjecture for an homogeneous space $X$, saying that if $X$has no non-trivial tame coverings then it has no non-trivial regular singular$\mathscr{O}_X$-coherent $\mathscr{D}_{X/k}$-modules. In order to do so weprove a K\"unneth formula for the regular singular stratified fundamental groupand a base change for Gauss-Manin stratifications in the non-proper case.

Gieseker conjecture for homogeneous spaces