A new proof of finiteness of maximal arithmetic reflection groups
[Une nouvelle preuve de finitude des groupes de réflexion arithmétiques maximaux]
Fisher, David1 ; Hurtado, Sebastian2
1 Rice University Math Department MS 136 P.O. Box 1892 Houston, TX 77005-1892 (USA)
2 Department of Mathematics PO Box 208283 New Haven, CT 06520-8283 Mailcode: 376 (USA)
Annales Henri Lebesgue, Tome 6 (2023), pp. 151-159

We give a new proof of the finiteness of maximal arithmetic reflection groups. Our proof is novel in that it makes no use of trace formulas or other tools from the theory of automorphic forms and instead relies on the arithmetic Margulis lemma of Fraczyk, Hurtado and Raimbault.

Nous donnons une nouvelle preuve de la finitude des groupes de réflexion arithmétiques maximaux. Notre preuve est nouvelle en ce qu’elle n’utilise pas de formules de traces ou d’autres outils de la théorie des formes automorphes et s’appuie à la place sur le lemme arithmétique de Margulis de Fraczyk, Hurtado et Raimbault.

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DOI : 10.5802/ahl.162
Classification : 20F60, 22F50, 37B05, 37C85, 37E10, 57R30
Keywords: Reflection groups, hyperbolic geometry

Fisher, David 1 ; Hurtado, Sebastian 2

1 Rice University Math Department MS 136 P.O. Box 1892 Houston, TX 77005-1892 (USA)
2 Department of Mathematics PO Box 208283 New Haven, CT 06520-8283 Mailcode: 376 (USA)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Fisher, David; Hurtado, Sebastian. A new proof of finiteness of maximal arithmetic reflection groups. Annales Henri Lebesgue, Tome 6 (2023), pp. 151-159. doi: 10.5802/ahl.162

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