19 problems

Let $b$ be an $ell$-block of a finite group $G$, let $D$ be a defect group for $b$, and let $b'$ be the Brauer-corresponding block of $\operatorname{N}_G(D)$. Let … be the subgroup…

Let $\Gamma\subseteq\operatorname{SL}_2(\mathbb{Z})$ be a congruence subgroup of prime level, and let $X(\Gamma)$ be the associated modular curve with Jacobian $J(\Gamma)$. Let…

Let $D$ be a triangle curve, meaning a smooth projective curve equipped with the relevant triangle-group covering structure, and consider its isomorphism class after forgetting the…

Let $\mathfrak M$ be the disjoint union of the coarse moduli spaces $\mathfrak M_{x,y}$ of canonical models of surfaces of general type with $\chi(\mathcal{O}_X)=x$ and $K_X^2=y$,…

Let $p$ be a prime, let $k$ be an algebraic closure of $\mathbb{F}_p$, let $\Gamma={\rm Gal}(k/\mathbb{F}_p)$, and let $\mathcal{C}$ be a finite category with $p$-orbit category…

Let $p$ be a prime, let $G$ be a finite group, and write $\mathcal{H}$ for the subgroup of the Galois group used in the McKay–Navarro formulation. Let $P\in\operatorname{Syl}_p(G)$…

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, set $\Delta=\Delta_d=(d+1)(d-3)$ and $K=\Q(\sqrt{\Delta})$. Let $\mathcal O_\Delta$ and $\mathcal O_K$ denote the quadratic order of discriminan…

Fix a positive integer $d\neq 3$, let $\Delta_d=(d+1)(d-3)$, and write $\Delta_d=f^2\Delta_0$, where $\Delta_0=\operatorname{disc}(\mathcal O_{K_d})$ and $K_d=\Q(\sqrt{\Delta_d})$.…

Suppose the semisimple local Langlands correspondence $bbLL_{bbG}$ exists. Let $bbsigma$ be an automorphism of $bbC$ fixing $bqsqrt q$, and let $(bbM,bbrho)$ be a supercuspidal-sup…

Galois-invariant normal Sylow subgroup conjecture. Let $G$ be a finite group and let $q$ be a prime. Then $G$ has a normal Sylow $q$-subgroup if and only if, for any $p\neq q$ that…

Fix a prime $p$ and a finite group $G$. Let $\mathcal{H}$ be the Galois automorphism group associated with the $p$-modular system in the source. Let $\mathcal{W}(G)$ be the set of…

Fix a prime $p$ and a finite group $G$. Let $\mathcal{H}=\operatorname{Gal}(\mathcal{K}/\mathbb{Q}_p)$ be the finite abelian group of Galois automorphisms associated with the $p$-m…

Let $(X,\Delta)$ be a log Fano pair defined over a field $k$, not necessarily algebraically closed, and consider test configurations of $(X,\Delta)$ that are defined over $k$. Galo…

Let $G$ be a finite group, let $p$ be a prime, and let $P$ be a Sylow $p$-subgroup of $G$. Let $B_0$ be the principal $p$-block of $G$ and $b_0$ the principal $p$-block of $N_G(P)$…

Let $p\in\{2,3\}$. Let $G$ be a finite group and let $B$ be a $p$-block of $G$ with nontrivial defect group $D$. Let $\sigma_1$ be the Galois automorphism introduced in the paper,…

Let $G$ be a finite group, let $p$ be a prime, and let $P$ be a Sylow $p$-subgroup of $G$. The exponent of the abelianization $P/P'$ should be determined by the action of certain G…

Let $\mathcal{L}$ be the lattice in complex Lorentz space and let $\Gamma_{\mathrm{DM}}$ be the automorphism group from Thurston's correspondence, with $\mathcal{L}_+$ the positive…

Let $G$ be the reductive group in the source, let $K$ be the chosen model of a maximal compact subgroup, and let $\Pi$ be an irreducible cohomological cuspidal automorphic represen…

Let $G$ be the reductive group in the source, let $K$ be the chosen model of a maximal compact subgroup, and let $M$ be a rational $G$-representation. For a factorizable automorphi…