# A trace formula for the distribution of rational $G$-orbits in ramified covers, adapted to representation stability

@article{Gadish2017ATF, title={A trace formula for the distribution of rational \$G\$-orbits in ramified covers, adapted to representation stability}, author={Nir Gadish}, journal={arXiv: Algebraic Geometry}, year={2017} }

A standard observation in algebraic geometry and number theory is that a ramified cover of an algebraic variety $\widetilde{X}\rightarrow X$ over a finite field $F_q$ furnishes the rational points $x\in X(F_q)$ with additional arithmetic structure: the Frobenius action on the fiber over $x$. For example, in the case of the Vieta cover of polynomials over $F_q$ this structure describes a polynomial's irreducible decomposition type.
Furthermore, the distribution of these Frobenius actions is…

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