  We report on a time regularity result for stochastic evolutionary PDEs with
monotone coefficients. If the diffusion coefficient is bounded in time without
additional space regularity we obtain a fractional Sobolev type time regularity
of order up to $\tfrac{1}{2}$ for a certain functional $ G( u )$ of the
solution. Namely, $ G( u )=\nabla u $ in the case of the heat equation and $G(
u )=|\nabla u |^{\frac{p-2}{2}}\nabla u $ for the $p$-Laplacian. The motivation
is twofold. On the one hand, it turns out that this is the natural time
regularity result that allows to establish the optimal rates of convergence for
numerical schemes based on a time discretization. On the other hand, in the
linear case, i.e. where the solution is given by a stochastic convolution, our
result complements the known stochastic maximal space-time regularity results
for the borderline case not covered by other methods.
