  We study the Schwinger mechanism by a uniform electric field in ${\rm dS}_2$
and ${\rm AdS}_2$ and the curvature effect on the Schwinger effect, and further
propose a thermal interpretation of the Schwinger formula in terms of the
Gibbons-Hawking temperature and the Unruh temperature for an accelerating
charge in ${\rm dS}_2$ and an analogous expression in ${\rm AdS}_2$. The exact
one-loop effective action is found in the proper-time integral in each space,
which is determined by the effective mass, the Maxwell scalar, and the scalar
curvature, and whose pole structure gives the imaginary part of the effective
action and the exact pair-production rate. The exact pair-production rate is
also given the thermal interpretation.
