TITLE: Compact generation for modular representations
QUESTION [10 upvotes]: Are the derived categories of modular representations of algebraic groups compactly generated? (e.g. consider SL_2 in characteristic 2). Note modular reps of finite groups are compactly generated (by the regular representation) - that's an example of compact generation of modules for an algebra. But here we're asking about comodules for a coalgebra that's not dualizable so it's not immediately clear (to me).
This makes more specific my other question for any "nice" examples of non-compactly generated categories.

REPLY [8 votes]: It appears this question is resolved in a definitive fashion in today's preprint
Algebraic Groups and compact generation of
their derived categories of representations by Hall and Rydh. Their first theorem asserts that the quasicoherent derived category of the stack $BG$ for $G$ a group scheme of finite type over a field $k$ is compactly generated if and only if either the characteristic of $k$ is zero, or the component group of the reductive part of $G$ (after
base change to $\overline{k}$) is SEMI-ABELIAN - or equivalently, contains no additive groups. In particular semisimple groups in (any) positive characteristic are out. 
They then deduce (using another paper of theirs from today, with Neeman) that even for $G$ affine in these ``poor" cases the quasicoherent derived category differs from the derived category of representations 
(ie quasicoherent sheaves on $BG$), and other striking results.