102 problems

Let $\Delta=(T_i,d_i,\lambda_i,\eta_i)_{1\leq i\leq k}\neq\Sigma_{\lambda,\eta}$ satisfy the setup and conditions of the cited theorems, and let $R_0(\Delta)$ be the refined expone…

Refined exponent conjecture. Under all the same conditions, the bound in Theorem may be tightened to

Let $\Delta=((T_i,d_i,\eta_i,\lambda_i))_i$ be a shape and let $\varphi_v$ be a trace-positive test function on $G_v$. For every $\psi=\bigoplus_i\psi_i[d_i]$ in $\Delta$, with…

Fix an imaginary CM field $F$ in which $p$ is unramified, let $F^+$ be its maximal totally real subfield, and set … Let $({\mathbb Z}^2_+)^S_0$ consist of tuples $a$ satisfying…

Pappas's spin flatness conjecture. The scheme $M_I$ is flat over $\mathcal O_E$; equivalently,

Let $E$ be the quadratic imaginary field in the paper, let $G_E$ be its absolute Galois group, and let $\pi$ be an automorphic representation of $\operatorname{U}(m)$ with regular…

Let $F$ be a $p$-adic field, let $E/F$ be a degree-two extension, let ${\rm U}(n)$ be the corresponding unitary group, and let $\pi$ be a representation of ${\rm GL}_n(E)$. A repre…

Genericity transfer conjecture. If $\pi_1\otimes\pi_2$ is an irreducible subrepresentation of this function space and $\pi_1$ is generic, then $\pi_2$ is also generic.

Let $\Gamma=([n],w)$ be an arbitrary hypergraph with non-negative weights. Let $\mathcal{KMP}_k$ be the discrete KMP process with $k$ indistinguishable particles on $\Gamma$, and l…

Let $\Gamma=([n],w)$ be an arbitrary hypergraph with non-negative weights. For each irreducible representation $\rho$ of $\mathrm{U}(n)$, let $\lambda_{\min}(\Gamma,\rho)$ denote t…

Let $F$ be a $p$-adic field, let $E$ and $K$ be quadratic field extensions of $F$, and let $V$ be an $n$-dimensional skew-hermitian space relative to $E/F$. Set $V_K=V\otimes_F K$,…

Let $\chi=\chi^{\phi,\lambda}$ be a primary irreducible character of $\mathrm{GU}_n(q)$, where $\phi$ is an orbit other than $\{\mathbf{1}\}$ and $\mathbf{1}$ is the trivial charac…

Let $\mathrm{GL}^\varepsilon_n$ denote the general linear group when $\varepsilon=1$ and the general unitary group when $\varepsilon=-1$, and let $\mathrm{GL}^\varepsilon_1$ be its…

Let $E$ be an imaginary quadratic field with odd discriminant $-D$, let $(L,\langle\phantom{x},\phantom{x}\rangle)$ be a Hermitian lattice over $\mathcal{O}_E$ of signature $(1,n)$…

Clozel–Harris–Taylor's generalized Ihara lemma. Then $V$ is Whittaker-generic.

Let $F/F_0$ be a quadratic extension, let $F'$ be the quadratic étale algebra associated with the unitary symmetric pair, and let $\pi_0$ be a cuspidal automorphic representation o…

Arithmetic twisted GGP conjecture. The following are equivalent:

Let $\pi$ be an irreducible cuspidal automorphic representation of $\mathrm U(V_{E_0})(\mathbb A_{E_0})$, let $\Pi$ be a weak base change of $\pi$ to $\mathrm {GL}_n(\mathbb A_E)$,…

Relative fundamental lemma in the semi-Lie case.

Oliver's p-group conjecture.

Let $F$ be a non-Archimedean local field, let $\boldsymbol{o}$ be its ring of integers, and use the notation $B(\gamma)^{\mathrm{irred}}$, $B(\gamma)^{\mathrm{split}}$, $d_i$,…

Let $L$ be a unimodular hermitian lattice over the ring of integers $\boldsymbol{o}_E$ of an unramified quadratic extension $E/F$, and let $M,M'$ be sublattices of $L$. Write…

Let $m\le n$ be fixed. Let $X'/X$ be the given double cover, let $\operatorname{U}_{2m}$ be the associated quasi-split unitary group, and let…

Scalar $P$-ordinary classicality conjecture. The restriction

Density conjecture. The space