  In this work, we give a proof of the globally sharp asymptotic profiles for
the spin-$\sfrak$ fields on a Schwarzschild background, including the scalar
field $(\sfrak=0)$, the Maxwell field $(\sfrak=\pm 1)$ and the linearized
gravity $(\sfrak=\pm 2)$. This confirms the conjectured Price's law in the
physics literature which predicts the sharp estimates of the spin $s=\pm
\sfrak$ components towards the future null infinity as well as in a compact
region. The asymptotics are derived via a unified, detailed analysis of the
Teukolsky master equation which is satisfied by all these components.
