  We consider the small quantum group u_q(G), for an almost-simple algebraic
group G over the complex numbers and a root of unity q of sufficiently large
order. We show that the Balmer spectrum for the small quantum group in type A
admits a continuous surjection P(\~N) \to Spec(stab u_q(G)) from the
(projectivized) Springer resolution. This surjection is shown to be a
homeomorphism over a dense open subset in the spectrum. In type A_1 we
calculate the Balmer spectrum precisely, where it is shown to be the
projectivized nilpotent cone. Our results extend to arbitrary Dynkin type
provided certain conjectures hold for the small quantum Borel. At the
conclusion of the paper we touch on relations with geometric representation
theory and logarithmic TQFTs, as represented in works of
Arkhipov-Bezrukavnikov-Ginzburg and Schweigert-Woike respectively.
