The Bernstein decomposition makes precise how the category of smooth complex representations of a p-adic reductive group G is built from supercuspidals. The center of the category factors accordingly and is largely well-understood. If one replaces the complex numbers by a coefficient field of characteristic p, the analogous category has strikingly different features. For one, the (Bernstein) center is rather small and often determined by the center of G. This was shown by Ardakov and Schneider for a general locally pro-p group G (under a mild hypothesis). In this talk, I will discuss the corresponding question in the derived setting. I will present various results related to the graded center of the derived category of smooth mod p representations. The talk is based on joint work (in progress) with Peter Schneider.