137 problems

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 $R$ and $S$ be isomorphic filtered $\lambda$-ring structures on … Let $\sigma:R\xrightarrow{\cong}S$ be an isomorphism. A filtered…

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…

Let $X$ be a smooth, projective, geometrically connected curve of genus $g$ defined over $\mathbb{Q}$. Let $K_4^{(3)}(X)$ denote the third Adams eigenspace of…

Let $(X,D)$ be a log smooth pair, and let $E_1\to E_2\to E_3\to E_1[1]$ be a distinguished triangle in $D(X\times^{\log}X)$ whose terms are strong log Fourier–Mukai kernels. Additi…

For an integer $n\geq 2$, let $R\Gamma(\mathbb{C}_p^\mathrm{Syn},\mathcal{O}\{n\})$ denote analytic syntomic cohomology of $\mathbb{C}_p$ with coefficients in the $n$-th Tate-twist…

Unitary Conjugation Groupoid Conjecture. There exists a natural assembly map

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

Let $\mu$ be a stability condition as in Assumption (stability), let $\alpha\in C(\mathcal A)_\mathrm{pe}$, and let $\varepsilon_\alpha^\mu\in K_\ast(\mathfrak M^\mathrm{rig})$ be…

Let $\mathcal A$ be the category under consideration, let $\alpha$ be a class and let $\mu$ be a stability condition, with $\varepsilon_\alpha^\mu$ the associated generalized $K$-t…

Let $C_2$ be the cyclic group of order two, let $\operatorname{MSpin}^c_{\operatorname{\mathbb{R}}}$ denote Real spin bordism, let $\mathcal{P}$ be the indexing set for the Anderso…

Type C K-Stanley expansion conjecture.

Let $Q$ be a quiver, let … is a free $R$-module. The conjecture is used to obtain the integral-form isomorphism with the positive half of the Maulik–Okounkov quantum loop group; th…

Freeness conjecture. For all $k\in\mathcal{M}(W)$, after possibly inverting $|W|$, the following hold: