Base-change compatibility of the new t-structure

From papers

Let AA be an associative algebra and consider

\bDren(\fD(\FlGaff)\critAmod).\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\otimes A\operatorname{mod}).

Equip it with the two t-structures described in the source: new1\mathrm{new}_1, obtained by tensoring the new t-structure on the affine-flag category with the usual t-structure on \bD(Amod)\bD(A\operatorname{mod}), and new2\mathrm{new}_2, generated by compact objects \CF\CF such that \CFJ\cla\CF\star J_\cla is nonpositive in the old t-structure. Base-change compatibility conjecture. The t-structures new1\mathrm{new}_1 and new2\mathrm{new}_2 coincide. The claim asserts stability of the new t-structure under tensoring with an arbitrary associative algebra; its resolution is not given.

Progress summary

Open

No public discussion or published progress appears to exist on this conjecture.

No public discussion or published progress was found.

Current status (as of August 2026): The conjecture remains open, with no recorded proof, counterexample, or substantive public progress.

Sources & referencesView supporting material

Primary source

Edward Frenkel and Dennis Gaitsgory, “D-modules on the affine flag variety and representations of affine Kac-Moody algebras”, arXiv:0712.0788 (2009).

Solutions 0

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