Addendum to: On volumes of arithmetic quotients of SO(1,n)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, pp. 263-268.

There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.

Classification : 11E57, 22E40 
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Belolipetsky, Mikhail. Addendum to: On volumes of arithmetic quotients of $SO(1,n)$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, pp. 263-268. http://www.numdam.org/item/ASNSP_2007_5_6_2_263_0/

[1] M. Belolipetsky, On volumes of arithmetic quotients of SO (1,n), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 3 (2004), 749-770. | Numdam | MR | Zbl

[2] A. Borel and G. Prasad, Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups, Inst. Hautes Études Sci. Publ. Math. 69 (1989), 119-171; Addendum, ibid. 71 (1990), 173-177. | Numdam | MR | Zbl

[3] M. Conder and C. Maclachlan, Compact hyperbolic 4-manifolds of small volume, Proc. Amer. Math. Soc. 133 (2005), 2469-2476. | MR | Zbl

[4] S. Lang, “Algebraic Number Theory”, Graduate Texts in Mathematics, Vol. 110. Springer-Verlag, New York, 1994. | MR | Zbl

[5] V. P. Platonov and A. S. Rapinchuk, “Algebraic Groups and Number Theory”, Pure and Applied Mathematics, Vol. 139. Academic Press, Inc., Boston, MA, 1994. | MR | Zbl

[6] A. Salehi Golsefidy, Lattices of minimum covolume in Chevalley groups over positive characteristic local fields, preprint. | MR | Zbl