Mathematics Problem Archive

f Γ is an irreducible arithmetic group of rank ≥ 2, then every homomorphism Γ→ ModS has finite image. For many arithmetic groups Γ the conjecture can ...

[Ehrenpreis Conjecture] Given two closed Riemann surfaces, there are finite un- branched covers with homeomorphic total spaces which are arbitrarily c...

(Orbit closures for moduli spaces). Determine the closures of the orbits for the GL+(2, R)-action on H(α) andQ(β). Are these closures always complex-a...

Let M = H3/Γ be a finite volume hyperbolic 3-manifold, does Γ contain a surface subgroup. This was answered in [ 8] for non-compact but finite volume ...

Forn> 3, does Aut(Fn) have property (T)? The corresponding question for mapping class groups is also open. If Aut( Fn) were to have Property (T), then...

Classify all finite loop spaces. This is the long term project of Bill Dwyer and Clarence Wilkerson. The theory, I believe, is that the Lie groups are...

Does the possible Kervaire-invariant-one element $\theta_6\in\pi_{126}^{S}$ exist; equivalently, is $h_6^2$ a permanent cycle in the mod-2 Adams spect...

We now know that Morava E-theory admits an action of the stabillizer group S. This is the famous Hopkins-Miller result, which one day I hope will see ...

Improve on Benson-Carlson-Rickard. Recall their theorem: if G is a finite p-group and k is an algebraically closed field, then thick subcategories in ...

Classify the localizing subcategories of the stable k[G]-module category. These should be in 1-1 correspondence with arbitrary subsets of Proj H^*(G,k...

Currently we know how to do equivariant stable homotopy theory only when the structure group G is compact Lie. But I bet we can do it when the group G...