ON THE ENUMERATION OF ORBITS OF UNIPOTENT GROUPS OVER FINITE FIELDS

Tobias Rossmann

doi:10.1090/proc/17030

ON THE ENUMERATION OF ORBITS OF UNIPOTENT GROUPS OVER FINITE FIELDS

Tobias Rossmann

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

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Abstract

We show that the enumeration of linear orbits and conjugacy classes of Z-defined unipotent groups over finite fields is "wild"in the following sense: given an arbitrary scheme Y of finite type over Z and integer n ≥1, the numbers #Y (Fq) mod qn can be expressed, uniformly in q, in terms of the numbers of linear orbits (or numbers of conjugacy classes) of finitely many Zdefined unipotent groups over Fq and finitely many Laurent polynomials in q.

Original language	English
Pages (from-to)	479-495
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	2
DOIs	https://doi.org/10.1090/proc/17030
Publication status	Published - Feb 2025

Keywords

average sizes of kernels
Conjugacy classes
linear orbits
unipotent groups

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10.1090/proc/17030

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abstract = "We show that the enumeration of linear orbits and conjugacy classes of Z-defined unipotent groups over finite fields is {"}wild{"}in the following sense: given an arbitrary scheme Y of finite type over Z and integer n ≥1, the numbers \#Y (Fq) mod qn can be expressed, uniformly in q, in terms of the numbers of linear orbits (or numbers of conjugacy classes) of finitely many Zdefined unipotent groups over Fq and finitely many Laurent polynomials in q.",

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N2 - We show that the enumeration of linear orbits and conjugacy classes of Z-defined unipotent groups over finite fields is "wild"in the following sense: given an arbitrary scheme Y of finite type over Z and integer n ≥1, the numbers #Y (Fq) mod qn can be expressed, uniformly in q, in terms of the numbers of linear orbits (or numbers of conjugacy classes) of finitely many Zdefined unipotent groups over Fq and finitely many Laurent polynomials in q.

AB - We show that the enumeration of linear orbits and conjugacy classes of Z-defined unipotent groups over finite fields is "wild"in the following sense: given an arbitrary scheme Y of finite type over Z and integer n ≥1, the numbers #Y (Fq) mod qn can be expressed, uniformly in q, in terms of the numbers of linear orbits (or numbers of conjugacy classes) of finitely many Zdefined unipotent groups over Fq and finitely many Laurent polynomials in q.

KW - average sizes of kernels

KW - Conjugacy classes

KW - linear orbits

KW - unipotent groups

UR - https://www.scopus.com/pages/publications/85215580095

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DO - 10.1090/proc/17030

M3 - Article

AN - SCOPUS:85215580095

SN - 0002-9939

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

ON THE ENUMERATION OF ORBITS OF UNIPOTENT GROUPS OVER FINITE FIELDS

Abstract

Keywords

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