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...

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?...

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....

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

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?...