  The present paper establishes new multiple procedures for simultaneous
testing of a large number of hypotheses under dependence. Special attention is
devoted to experiments with rare false hypotheses. This sparsity assumption is
typically for various genome studies when a portion of remarkable genes should
be detected. The aim is to derive tests which control the false discovery rate
(FDR) always at finite sample size. The procedures are compared for the set up
of dependent and independent $p$-values. It turns out that the FDR bounds
differ by a dependency factor which can be used as a correction quantity. We
offer sparsity modifications and improved dependence tests which generalize the
Benjamini-Yekutieli test and adaptive tests in the sense of Storey. As a
byproduct, an early stopped test is presented in order to bound the number of
rejections. The new procedures perform well for real genome data examples.
