2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101139Let $X$ be a smooth projective geometrically connected curve over a finite field with function field $K$. Let $\G$ be a connected semisimple group scheme over $X$. Under certain hypothesis we prove the equality of two numbers associated with $\G$. The first is an arithmetic invariant, its Tamagawa number. The second, is a geometric invariant, the number of connected components of the moduli stack of $\G$-torsors on $X$.Revised versionNumber TheoryAlgebraic GeometryRepresentation Theorytext