137 problems

HK conjecture. For $* = 0,1$, there is an isomorphism

Coarse Baum–Connes conjecture with coefficients. The homomorphism

Let $X$ be a smooth 3-fold and let $\mathscr{L}_1,\mathscr{L}_2$ be line bundles on $X$ satisfying … Let…

Let $n$ be an integer with $n\geq 3$, and let $R$ and $S$ be isomorphic filtered $\lambda$-ring structures on … Let $\sigma:R\xrightarrow{\cong}S$ be an isomorphism. A filtered…

Type C K-Stanley expansion conjecture.

Coarse Baum–Connes and coarse Novikov conjectures. The coarse Baum–Connes conjecture claims that $\mu$ is an isomorphism, while the coarse Novikov conjecture claims that $\mu$ is i…

Goncharov's conjecture. For any field $\mathbb K$ there is a functorial isomorphism

Independence conjecture. The series $\mathsf{DT}_{r,k}^{\rm ell}(\mathbb{A}^3,q,t,w;p)$ does not depend on the elliptic parameter $p$.

Rough Baum–Connes conjecture. The map $\mu_u$ is an isomorphism. This conjecture asserts that uniform $K$-homology of the Rips complexes computes the $K$-theory of the uniform Roe…

Weinberger–Yu's conjecture. The group $\mathcal M_{\gamma_1,\ldots,\gamma_n}$ has rank $n$, and every nonzero element of it lies outside the image of the assembly map

Boundary coarse Baum–Connes conjecture. This assembly map is an isomorphism. This conjecture concerns the boundary version of the coarse Baum–Connes conjecture and is used in appli…

Affine Grothendieck polynomial conjecture. The $K$-theory class of the structure sheaf of $\Pi_f$ is the image of $\tilde{G}_f$ under this identification:

Let $X_1$ and $X_2$ be the two components arising when a puzzle variety breaks in the geometric Littlewood–Richardson degeneration, and let $X_3$ be the puzzle variety correspondin…

Twisted Bost conjecture. The map $\mu_\sigma^{\mathcal A}$ is an isomorphism for $j=0,1$. The conjecture is presented as an unconditional analogue of the twisted Baum–Connes conjec…

Combinatorial characterization conjecture. If the assignment $M\mapsto G_M$ satisfies 1. for every such decomposition,

Gamma-polynomial conjecture.

K-theoretic matroid invariant conjecture. For any matroids $M$, $M_1$, and $M_2$,

Let $S_n$ be the symmetric group, let ${\cal G}_w(x_1,\ldots,x_n)$ be the Grothendieck polynomial associated with $w\in S_n$, and let $G_i^{A_{n-1}}$ be the elements defined by…

Let $n$ be an integer with $n\geq 3$, and let … be a family of nonzero integers. A filtered $\lambda$-ring structure on $\mathbf{Z}[x]/(x^n)$ has prescribed Adams linear coefficien…

Let $n$ be an integer with $n\geq 3$. Consider the filtered truncated polynomial ring … A filtered $\lambda$-ring structure is a filtered $\lambda$-ring structure on this ring, and…

Let $K\subset\mathbb C_p$ be a discrete valuation subfield, meaning that its valuation is induced from the valuation on $\mathbb C_p$, and let $R$ be the valuation ring of $K$. Ass…

Let $M$ be a symplectic manifold, let ${\cal W}$ be its Weyl algebra bundle, and let $(\Omega(M, {\cal W}), \nabla, R)$ be the associated $Q$-algebra. A finitely generated projecti…

Let $E$ be an elliptic curve over a field $k$, let $B(E,3)$ denote the elliptic Bloch complex, and let ${\cal M}{\cal M}_k$ be the hypothetical abelian category of mixed motivic sh…

Let $\lambda$ and $\mu$ be partitions, and let $\widetilde G_\lambda(\mathbf x)$ denote the stable Grothendieck polynomial. Write $\lambda\vee\mu$ and $\lambda\wedge\mu$ for the jo…

Let $u,v\in S_n$ be vexillary permutations, let $\phi(w)$ be the Wachs flag of $w$, and write $a\preceq b$ when $a$ is a prefix of $b$. Let $\mathfrak G_w^{(\beta)}(\mathbf x)$ be…