  The reduction of 4d matter-gravity theory to $S_2$, $H_2$ or $R_2$ leads to
effective 2d dilatonic gravity with dilaton coupled matter. Spinors give the
exceptional example of the theory which is conformally invariant in 4d as well
as in 2d, after reduction. We find 4d and 2d conformal anomaly induced
effective action (EA) for Majorana spinor. It is expected for some time that
s-wave EA (i.e. the one for dilaton coupled 2d matter) is some (s-wave)
approximation to 4d EA. We compare such 2d and 4d spinor EAs on the same
gravitational background and argue that s-wave EA indeed qualitatively
corresponds to no higher derivatives approximation for 4d EA.
