Freeness conjecture for the stalks of standard sheaves

Let I!(λ,Z)\mathcal I_!(\lambda,\mathbb Z) be the standard sheaf associated with a dominant coweight λ\lambda in the geometric Satake correspondence. Its stalks are free abelian groups.

Freeness conjecture. The stalks of I!(λ,Z)\mathcal I_!(\lambda,\mathbb Z) are free.

This conjecture concerns the integral structure of standard sheaves in the affine Grassmannian and would ensure that their local data has no torsion. The supplied text does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

I. Mirkovic and K. Vilonen, “Geometric Langlands duality and representations of algebraic groups over commutative rings”, arXiv:math/0401222 (2018).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.