Mathematics Problem Archive

Bass conjecture: for every finitely generated $\mathbb Z$-algebra $A$ and every $n\geq0$, is the G-theory group $K'_n(A)$ finitely generated? Equivale...

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...

Deligne's conjecture on Hochschild cohomology about the operadic structure on Hochschild cochain complex....

Fröberg conjecture on the Hilbert functions of a set of forms....

Fujita conjecture regarding the line bundle $K_{M} \otimes L^{\otimes m}$ constructed from a positive holomorphic line bundle $L$ on a compact complex...

General elephant problem: do general elephants have at most Du Val singularities?...

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...

Nagata's conjecture on curves, specifically the minimal degree required for a plane algebraic curve to pass through a collection of very general point...

Nagata–Biran conjecture that if $X$ is a smooth algebraic surface and $L$ is an ample line bundle on $X$ of degree $d$, then for sufficiently large $r...

Nakai conjecture: if a complex algebraic variety has a ring of differential operators generated by its contained derivations, then it must be smooth....

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

Section conjecture on splittings of group homomorphisms from fundamental groups of complete smooth curves over finitely-generated fields $k$ to the Ga...

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

Zariski multiplicity conjecture on the topological equisingularity and equimultiplicity of varieties at singular points...

Are infinite sequences of flips possible in dimensions greater than 3?...

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