Arithmetic Fake Projective Spaces and Arithmetic Fake Grassmannians
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منابع مشابه
Arithmetic of a fake projective plane and related elliptic surfaces
The purpose of the present paper is to explain the fake projective plane constructed by J. H. Keum from the point of view of arithmetic ball quotients. Beside the ball quotient associated with the fake projective plane, we also analize two further naturally related ball quotients whose minimal desingularizations lead to two elliptic surfaces, one already considered by J. H. Keum as well as the ...
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We will say that a smooth complex projective algebraic variety V (of dimension n− 1) is a fake Pn−1 if V is the quotient of the unit ball Bn−1 in Cn−1by a torsion-free cocompact discrete subgroup of PU(n−1, 1), and all the Betti numbers of V are equal to those of Pn−1 C . If the fundamental group of a fake Pn−1 is an arithmetic subgroup of PU(n − 1, 1), then we will say that it is an arithmetic...
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We will say that a smooth projective complex algebraic variety V (of dimension n − 1) is a fake Pn−1 if V is the quotient of the unit ball Bn−1 by a torsion-free cocompact discrete subgroup of PU(n − 1, 1), and all the Betti numbers of V are equal to those of Pn−1 C . If the fundamental goup of a fake P n−1 is an arithmetic subgroup of PU(n − 1, 1), then we will say that it is an arithmetic fak...
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In [CMSZ2], Cartwright, Mantero, Steger, and Zappa discovered a unitary group in three variables with respect to the quadratic extension Q( √ −15)/Q whose integral model over the integer ring with the prime 2 inverted gives rise to a diadic discrete group acting transitively on vertices of Bruhat-Tits building over Q2. Inside the integral model are three subgroups to which the restricted action...
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In this paper we consider Property (FA) for lattices in SU(2, 1). First, we prove that SU(2, 1;O3) has Property (FA). We then prove that the arithmetic lattices in SU(2, 1) of second type arising from congruence subgroups studied by Rapoport–Zink and Rogawski cannot split as a nontrivial free product with amalgamation; one such example is Mumford’s fake projective plane. In fact, we prove that ...
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