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41.
T. N. Venkataramana 《Compositio Mathematica》2001,125(2):221-253
We obtain a necessary condition for a cohomology class on a compact locally symmetric space S()=X (a quotient of a symmetric space X of the non-compact type by a cocompact arithmetic subgroup of isometries of X) to restrict non-trivially to a compact locally symmetric subspace S
H()=Y of X. The restriction is in a 'virtual' sense, i.e. it is the restriction of possibly a translate of the cohomology class under a Hecke correspondence. As a consequence we deduce that when X and Y are the unit balls in
n
and
m
, then low degree cohomology classes on the variety S() restrict non-trivially to the subvariety S
H
(); this proves a conjecture of M. Harris and J-S. Li. We also deduce the non-vanishing of cup-products of cohomology classes for the variety S(). 相似文献
42.
T. N. Venkataramana 《Inventiones Mathematicae》2014,197(1):1-45
We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of ramification points is sufficiently large compared to the degree d and the ramification degrees are co-prime to d. 相似文献