  This talk presents the detection issues for the lightest slepton
\tilde{\tau}_1 at a future e+e- TeV collider given the dark matter constraints
set on the SUSY mass spectrum by the WMAP results. Two methods for measuring
its mass m_{\tilde{\tau}_1} and the resulting precision on the dark matter
density are briefly discussed in the SUSY mSUGRA scenario with R-parity
conservation when the mass difference between m_{\tilde{\tau}_1} and that of
the lightest neutralino is small (a few GeV). The analysis is performed with
TESLA parameters in both head-on and crossing angle modes.
