  In this note, we consider the Lyndon--Hochschild--Serre spectral sequence
corresponding to the first Frobenius kernel of an algebraic group G, computing
the extensions between simple $G$-modules. We state and discuss a conjecture
that $E_2=E_\infty$ and provide general conditions for low-dimensional terms on
the $E_2$-page to be the same as the corresponding terms on the
$E_{\infty}$-page, i.e. its abutment.
