106 problems

Beilinson–Parshin conjecture. One should have

First Kac-Weisfeiler conjecture. The equality

Thakur's basis conjecture. The values $\zeta_{A}(\mathfrak{s})$ for $\mathfrak{s} \in \mathcal{I}^{\mathrm{T}}$ form a basis of $\mathcal{Z}_{k}$.

Let $K$ be a field of characteristic $p>0$, and let $f_k\in K\{x_1,\ldots,x_n\}$ be a sequence of isolated singularities whose Milnor numbers tend to infinity as $k\to\infty$. The…

BEO's classification conjecture. Every symmetric tensor category of moderate growth over $\mathbf{k}$ is a representation category over the symmetric tensor category…

Let $X$ be a variety over an algebraically closed field $K$ of characteristic $p>0$, let $f$ be a rational self-map of $X$, let $x\in X(K)$ be a closed point whose orbit…

Let $k$ be an algebraically closed field of characteristic $p\neq 0$. For a nonnegative integer $r$, let $L_{k,r}$ denote the class of nonsingular curves over $k$ whose associated…

Let $\mathbb{F}_q$ be a finite field of characteristic $p$, let $E/\mathbb{F}_q(T)$ be an elliptic curve, and let $P,Q\in E(\mathbb{F}_q(T))$ be nontorsion points. Positive common-…

Pascal Finite Generators Conjecture. Every element of $\operatorname{Aut}_{su}(K,n)$ belongs to $\langle PF(K,n)\rangle_{\circ}$.

Reductive local structure conjecture. Under these hypotheses, such an étale morphism exists.

Let $F$ be a non-Archimedean local field, let $G=\operatorname{GL}_n(F)$, and let $C^{-\infty}(G)$ denote the space of generalized functions on $G$, with…

Involution compatibility conjecture. For every $\mathfrak{s}\in\mathcal{I}$,

Infinite collision conjecture. The set $C(\alpha_1,\alpha_2;\beta)$ is infinite. The conjecture reverses the expectation stated immediately beforehand, which predicted finiteness w…

General colliding-orbits conjecture. If $C(\alpha_1,\alpha_2;\beta)$ is infinite, then at least one of the following holds: (1) there is a family of polynomials $g_\lambda(x)$, int…

Let $X$ be a smooth complete curve over a field $k$, let $G$ be a reductive group, and let $\Shv_{\Nilp}(\Bun_G)$ be the category of $\ell$-adic sheaves on $\Bun_G$ with nilpotent…

Contact-inequivalence conjecture. For general $a,b,c,d ain F$, these singularities are not contact equivalent.

Let $p$ be an odd prime. Let $X'$ be a smooth curve of genus $3$ over $\overline{\mathbf F}_p$, and let $\pi':Y'\to X'$ be a double cover branched at two points. By the Riemann–Hur…

Let $p$ be a prime congruent to $1$ modulo $4$. Consider unramified double covers of smooth curves of genus $3$; such a cover has a smooth curve of genus $5$ as its total space. Su…

Let $K$ be the base field. A $T$-prime algebra is an algebra whose polynomial identities form a prime $T$-ideal, and the twisted tensor product is the product considered for $[?]$-…

Positive-characteristic dynamical Mordell–Lang conjecture. The return set $R$ is a union of finitely many infinite arithmetic progressions together with finitely many sets of the f…

Same-degree intersection-of-orbits conjecture. At least one of the following holds: (1) there exists $m\in{\mathbb N}$ such that $f^m=g^m$; or (2) there exist linear polynomials…

Intersection-of-orbits conjecture. At least one of the following holds: (1) there exist $m,n\in{\mathbb N}$ such that $f^m=g^n$; or (2) there exist linear polynomials…

Let $A$ be an algebra over a field $k$ of characteristic $p$. Let $\mathscr{D}_A$ denote the ring of differential operators on $A$, and let the Hasse–Schmidt derivations on $A$ be…

Let $K$ be a field of characteristic $p$, let $X$ be a quasi-projective variety defined over $K$, let $\Phi$ be an endomorphism of $X$, let $\alpha\in X(K)$, and let $V\subseteq X$…

Let $\overline{K}$ be an algebraically closed field of characteristic $p$, and let the paper's singularity-classification algorithm be denoted by Algorithm 1. Positive-characterist…