arXiv Open Access 2015

Counting points of schemes over finite rings and counting representations of arithmetic lattices

Avraham Aizenbud Nir Avni

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Abstrak

We relate the singularities of a scheme $X$ to the asymptotics of the number of points of $X$ over finite rings. This gives a partial answer to a question of Mustata. We use this result to count representations of arithmetic lattices. More precisely, if $Γ$ is an arithmetic lattice whose $\mathbb{Q}$-rank is greater than one, let $r_n(Γ)$ be the number of irreducible $n$-dimensional representations of $Γ$ up to isomorphism. We prove that there is a constant $C$ (for example, $C=746$ suffices) such that $r_n(Γ)=O(n^C)$ for every such $Γ$. This answers a question of Larsen and Lubotzky.

Topik & Kata Kunci

math.GR math.AG math.NT math.RT

Penulis (2)

Avraham Aizenbud

Nir Avni

Format Sitasi

APA MLA BibTeX

Aizenbud, A., Avni, N. (2015). Counting points of schemes over finite rings and counting representations of arithmetic lattices. https://arxiv.org/abs/1502.07004

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Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓