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We prove the existence of a Galois closure for towers of torsors under finitegroup schemes over a proper, geometrically connected and geometrically reducedalgebraic stack $X$ over a field $k$. This is done by describing the Norifundamental gerbe of an essentially finite cover of $X$. A similar result isalso obtained for the $S$-fundamental gerbe.

Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors