  We present a topological multiple testing scheme for detecting peaks on the
sphere under isotropic Gaussian noise, where tests are performed at local
maxima of the observed field filtered by the spherical needlet transform. Our
setting is different from the standard Euclidean/large same asymptotic
framework, yet highly relevant to realistic experimental circumstances for some
important areas of application in astronomy. More precisely, we focus on cases
where a single realization of a smooth isotropic Gaussian random field on the
sphere is observed, and a number of well-localized signals are superimposed on
such background field. The proposed algorithms, combined with the
Benjamini-Hochberg procedure for thresholding p-values, provide asymptotic
strong control of the False Discovery Rate (FDR) and power consistency as the
signal strength and the frequency of the needlet transform get large. This
novel multiple testing method is illustrated in a simulation of point-source
detection in Cosmic Microwave Background radiation (CMB) data.
