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On volumes of arithmetic quotients of S O ( 1 , n )

Mikhail Belolipetsky (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of S O ( 1 , n ) . As a result we prove that for any even dimension  n there exists a unique compact arithmetic hyperbolic n -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...

On Witt rings of function fields of real analytic surfaces and curves.

Piotr Jaworski (1997)

Revista Matemática de la Universidad Complutense de Madrid

Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...

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