Mathematics Problem Archive

Bass–Quillen conjecture: if $A$ is a regular Noetherian ring, is every finitely generated projective module over $A[t_1,\ldots,t_n]$ extended from a p...

In spherical or hyperbolic geometry, must polyhedra with the same volume and Dehn invariant be scissors-congruent?...

Maulik–Nekrasov–Okounkov–Pandharipande conjecture on an equivalence between Gromov–Witten theory and Donaldson–Thomas theory...

Parshin's conjecture: the higher algebraic K-groups of any smooth projective variety defined over a finite field must vanish up to torsion....

Virasoro conjecture: a certain generating function encoding the Gromov–Witten invariants of a smooth projective variety is fixed by an action of half ...

Prove resolution of singularities for algebraic varieties over fields of positive characteristic in arbitrary dimension....