Polynomiality of the faithful dimension for nilpotent groups over finite truncated valuation rings

DOI10.1090/tran/9032arXiv2204.12412OpenAlexW4385489936MaRDI QIDQ6062128

Mohammad Bardestani, Keivan Mallahi Karai, Dzmitry Rumiantsau, Hadi Salmasian

Publication date: 30 November 2023

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.12412

zbMATH Keywords

faithful dimension, \(p\)-group, nilpotent group, Lazard correspondence

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05) Rational points (14G05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some consequences of the Karpenko-Merkurjev theorem.
• Essential dimension of finite \(p\)-groups.
• The orbit method for profinite groups and a \(p\)-adic analogue of Brown's theorem.
• A remark on Ax's theorem on solvability modulo primes
• Kirillov theory for compact p-adic groups
• Proof of Springer's hypothesis
• Essential dimension: A functorial point of view (after A. Merkurjev)
• Diophantine approximation on matrices and Lie groups
• Sets of primes determined by systems of polynomial congruences
• Representation zeta functions of compact \(p\)-adic analytic groups and arithmetic groups
• The elementary theory of finite fields
• Solving diophantine problems modulo every prime
• Strictly local solutions of diophantine equations
• Functional equations for local normal zeta functions of nilpotent groups. With an appendix by A. Beauville.
• Minimal dimension of faithful representations for \(p\)-groups
• Enumerating classes and characters of 𝑝-groups
• Zeta functions of groups and enumeration in Bruhat-Tits buildings
• Kirillov's orbit method and polynomiality of the faithful dimension of $p$-groups
• Essential dimension
• Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B
• Irreducible Subvarieties and Rational Points
• Diophantine Problems Over Local Fields I
• Commutative Artinian Principal Ideal Rings
• Number fields
• Weighted Ehrhart series and a type-\(\mathsf{B}\) analogue of a formula of MacMahon

This page was built for publication: Polynomiality of the faithful dimension for nilpotent groups over finite truncated valuation rings