Over Q, degree 3 polynomial invariants separate orbits of C_p representations; a new Galois-descent condition yields analogous degree bounds for abelian groups over non-closed fields.
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Separating polynomial invariants over non-closed fields of finite abelian groups
Over Q, degree 3 polynomial invariants separate orbits of C_p representations; a new Galois-descent condition yields analogous degree bounds for abelian groups over non-closed fields.