Journal
DUKE MATHEMATICAL JOURNAL
Volume 167, Issue 14, Pages 2721-2743Publisher
DUKE UNIV PRESS
DOI: 10.1215/00127094-2018-0021
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Funding
- Israel Science Foundation [687/13]
- National Science Foundation (NSF) [DMS-1100943, DMS-0901638, DMS-1303205]
- United States-Israel Binational Science Foundation (BSF) [2012247]
- Minerva foundation grant
- BSF [2012247]
- Office of Polar Programs (OPP)
- Directorate For Geosciences [2012247] Funding Source: National Science Foundation
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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 Gamma is an arithmetic lattice whose Q-rank is greater than 1, then let r(n) (Gamma) be the number of irreducible n-dimensional representations of Gamma up to isomorphism. We prove that there is a constant C (in fact, any C > 40 suffices) such that r(n) (Gamma) = O(n(C)) for every such Gamma. This answers a question of Larsen and Lubotzky.
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