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pro vyhledávání: '"Emery, Vincent"'
Autor:
Emery, Vincent
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
Externí odkaz:
http://arxiv.org/abs/2308.03752
We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/1911.01170
Autor:
Emery, Vincent, Mila, Olivier
We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $\mathrm{PO}(n,1)$ with $n>3$. We further show that under an additional assumption (satisfied in all known cases), the covolumes of these lattices c
Externí odkaz:
http://arxiv.org/abs/1810.12837
Autor:
Emery, Vincent, Kim, Inkang
For any n>1 we determine the uniform and nonuniform lattices of the smallest covolume in the Lie group Sp(n,1). We explicitly describe them in terms of the ring of Hurwitz integers in the nonuniform case with n even, respectively, of the icosian ring
Externí odkaz:
http://arxiv.org/abs/1802.07776
Autor:
Emery, Vincent
Publikováno v:
Sel. Math. New Ser. (2017) 23: 2849
We prove that the covolume of any quasi-arithmetic hyperbolic lattice (a notion that generalizes the definition of arithmetic subgroups) is a rational multiple of the covolume of an arithmetic subgroup. As a corollary, we obtain a good description fo
Externí odkaz:
http://arxiv.org/abs/1603.07349
In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an applicatio
Externí odkaz:
http://arxiv.org/abs/1506.03727
Autor:
Emery, Vincent
We obtain upper bounds for the torsion in the $K$-groups of the ring of integers of imaginary quadratic number fields, in terms of their discriminants.
Comment: 6 pages. Version 2 corrects a few typos and syntax mistakes
Comment: 6 pages. Version 2 corrects a few typos and syntax mistakes
Externí odkaz:
http://arxiv.org/abs/1504.01912
Publikováno v:
Documenta Math. Extra Volume: Merkurjev (2015) 71--83
Elaborating on a method of Soul\'e, and using better estimates for the geometry of hermitian lattices, we improve the upper bounds for the torsion part of the K-theory of the rings of integers of number fields.
Comment: 11 pages. Minor change
Comment: 11 pages. Minor change
Externí odkaz:
http://arxiv.org/abs/1406.5953
Autor:
Belolipetsky, Mikhail, Emery, Vincent
Publikováno v:
Documenta Mathematica 19 (2014) 801-814
We conjecture that for every dimension n not equal 3 there exists a noncompact hyperbolic n-manifold whose volume is smaller than the volume of any compact hyperbolic n-manifold. For dimensions n at most 4 and n=6 this conjecture follows from the kno
Externí odkaz:
http://arxiv.org/abs/1310.2270
Autor:
Emery, Vincent
Publikováno v:
Algebr. Geom. Topol. 14 (2014) 853-861
We prove that for n>4 there is no compact arithmetic hyperbolic n-manifold whose Euler characteristic has absolute value equal to 2. In particular, this shows the nonexistence of arithmetically defined hyperbolic rational homology n-sphere with n eve
Externí odkaz:
http://arxiv.org/abs/1304.3509