• Corpus ID: 9990137

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}
}
  • Nir Gadish
  • Published 6 March 2017
  • Mathematics
  • arXiv: Algebraic Geometry
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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References

SHOWING 1-10 OF 10 REFERENCES

Representation stability in cohomology and asymptotics for families of varieties over finite fields

We consider two families X_n of varieties on which the symmetric group S_n acts: the configuration space of n points in C and the space of n linearly independent lines in C^n. Given an irreducible

FI-modules and stability for representations of symmetric groups

In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordered points on an

Representation Stability for Families of Linear Subspace Arrangements

Linear representations of finite groups

Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples. Representations in characteristic zero:

Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t]

TLDR
A function field analogue of classical problems in analytic number theory, concerning the autocorrelations of divisor functions, in the limit of a large finite field is solved.

Formule de Lefschetz et rationalité des fonctions $L$

© Association des collaborateurs de Nicolas Bourbaki, 1966, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions

Zeta functions and L-functions

  • Lei Fu
  • Mathematics
    Handbook of Finite Fields
  • 2013