scholarly journals Locally symmetric spaces andK–theory of number fields

2012 ◽  
Vol 12 (1) ◽  
pp. 155-213
Author(s):  
Thilo Kuessner
Keyword(s):  
Symmetric Spaces ◽  
Number Fields ◽  
Locally Symmetric Spaces

Cycles and Harmonic Forms on Locally Symmetric Spaces

1985 ◽  
Vol 28 (1) ◽  
pp. 3-38 ◽  
Author(s):  
John J. Millson
Keyword(s):  
Quadratic Forms ◽  
Symmetric Spaces ◽  
Number Fields ◽  
The Other ◽  
Weil Representation ◽  
Harmonic Forms ◽  
Congruence Subgroups ◽  
Locally Symmetric Spaces ◽  
Background Material ◽  
Totally Real

AbstractTwo constructions of cohomology classes for congruence subgroups of unit groups of quadratic forms over totally real number fields are given and shown to coincide. One is geometric, using cycles, and the other is analytic, using the oscillator (Weil) representation. Considerable background material on this representation is given.

scholarly journals Brauer equivalent number fields and the geometry of quaternionic Shimura varieties

2018 ◽  
Vol 70 (2) ◽  
pp. 675-687
Author(s):  
Benjamin Linowitz
Keyword(s):  
Symmetric Spaces ◽  
Number Fields ◽  
Shimura Varieties ◽  
Brauer Groups ◽  
Locally Symmetric Spaces ◽  
Totally Geodesic ◽  
Equivalent Number ◽  
Geodesic Surfaces

Abstract Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper, we prove a variety of number theoretic results about Brauer equivalent number fields (for example, they must have the same signature). These results are then applied to the geometry of certain arithmetic locally symmetric spaces. As an example, we construct incommensurable arithmetic locally symmetric spaces containing exactly the same set of proper immersed totally geodesic surfaces.

scholarly journals Lp spectral theory and heat dynamics of locally symmetric spaces

2010 ◽  
Vol 258 (4) ◽  
pp. 1121-1139 ◽  
Author(s):  
Lizhen Ji ◽  
Andreas Weber
Keyword(s):  
Spectral Theory ◽  
Symmetric Spaces ◽  
Locally Symmetric Spaces

scholarly journals Two natural generalizations of locally symmetric spaces

1992 ◽  
Vol 2 (1) ◽  
pp. 57-80 ◽  
Author(s):  
Jürgen Berndt ◽  
Lieven Vanhecke
Keyword(s):  
Symmetric Spaces ◽  
Locally Symmetric Spaces
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