10 problems

The geometric conjecture. There is an isomorphism

ABPS conjecture. Such a continuous parametrisation can always be constructed. The conjecture concerns the topology of the tempered Iwahori-spherical dual and would extend the known…

Let $(M',\xi_M,\mathcal T_M,\bar h_M)$ be a Levi subgroup of $(G',\xi,\mathcal T,\bar h)$, let $s=(M',\sigma)$ be a cuspidal datum for $G'$, and let $\hat s=({}^LM,\psi,v,\varrho)$…

Let ${\mathcal H}$ be a connected reductive group over a local non-archimedean field. Let $\mathfrak{Lev}({\mathcal H})$ represent the conjugacy classes of Levi subgroups, let…

Let $G$ be a reductive $p$-adic group, let $L$ be a Levi subgroup, and let ${\mathfrak s}^{\vee}=[L^{\vee},\psi,\varepsilon]_{G^{\vee}}\in{{\mathfrak B}}^{\vee}(G)$ be a Bernstein…

Let $F$) be a non-archimedean local field and $G$ a connected reductive algebraic group over $F$. For a Levi subgroup $L$ of $G$, write $W(G,L)=N_G(L)/L$. For an inertial equivalen…

ABPS conjectures. There exists a bijection

Let ${\mathcal G}$ be a reductive $p$-adic group and let ${\mathfrak s}$ be a point in the Bernstein spectrum of ${\mathcal G}$. Let…

Let ${\mathcal G}$ be a reductive $p$-adic group and let ${\mathfrak s}$ be a point in its Bernstein spectrum. The corresponding Bernstein component…

Geometric structure conjecture. After a simple algebraic deformation, the space ${\mathfrak A}(G)$ is a model of the smooth dual ${\rm Irr}(G)$.