43 problems

Let $g$ be the genus, let $\mathfrak{t}_g$ be the relevant graded Lie algebra associated to the Torelli group, and let $\mathfrak{m}_g$ be the Lie algebra of symplectic derivations…

Let the Deligne–Ihara graded Lie algebra be the $p$-graded Lie algebra defined, analogously to $g aiveotimes Qp$, using the pro-$p$ outer Galois representation of…

Let $\mathcal{I}_{g,1}$ be the Torelli group of a genus-$g$ surface with one boundary component, and let $\operatorname{gr}(\mathcal{I}_{g,1})$ be the graded rational Lie algebra a…

Let ${\mathfrak h}^{\mathbb Q}_{g,1}$ be the rational graded Lie algebra of symplectic derivations, let $H_{\mathbb Q}$ be the rational symplectic module, and let…

Let $\mathfrak h_{g,1}^{\mathbb Q}$ be the graded Lie algebra under consideration, and let $\operatorname{Sp}$ act on it through the symplectic action on $H_{\mathbb Q}$. Define…

Ihara's conjecture. The induced map

Ihara–Deligne conjecture. The graded Lie algebra

Let $T=\mathbb{P}^{1}_{\mathbb{Q}}-\{0,1,\infty\}$, and let $\mathfrak{t}=\bigoplus_{m>0}\mathfrak{t}_m$ be the graded Lie algebra over $\mathbb{Z}_p$ associated with the lower cen…

Let $X$ be the once-punctured elliptic curve under consideration, let $K$ be its complex multiplication field, let $I_K$ be the specified index set, and let $\boldsymbol{m}$ range…

Let $\mathfrak{g}$ be a complex finite-dimensional Lie algebra, and let $(\mathcal{M},\delta)$ be an abelian magma such that $\mathfrak{g}$ is $\mathcal{M}$-magma-graded, with the…

Let $\theta:G\to G$ be an automorphism of order $m\in\mathbb{Z}_{>0}$, let $G_0$ be the neutral component of $G^\theta$, and let $\mathfrak{g}_1$ be the $\zeta_m$-eigenspace of…

Let $\fg$ be a simple $\mathbb{Z}$-graded Lie algebra of polynomial growth (GLAPG type). Let $\fvect(1):=\fder\,\Cee[x]$ and $\fwitt$, equivalently…

Let $I$ be the index set of multi-indices used to define the characters $kappa_{\boldsymbol{m}}$, let $g$ be the associated graded Lie algebra, and let $chi^{\boldsymbol{m}}$ denot…

Let $\xi_B$ and $\xi_D$ be the block-graded and depth-graded functionals associated with the relations in the preceding block-to-depth reduction theorem, and let $\sigma$ be an ele…

Depth-to-even-block isomorphism conjecture. The map ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}\to{\mathfrak{e}}{\mathfrak{b}}{\mathfrak{g}}$ is an isomorphism. It is stated to hol…

Let ${\mathfrak{d}}{\mathfrak{g}}$ be the depth graded motivic Lie algebra, let ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}$ be the subalgebra generated by the non-exceptional elem…

Let ${\mathfrak{d}}{\mathfrak{g}}$ be the depth graded motivic Lie algebra, and let $\mathrm{S}$ be the space of cusp forms for $\mathrm{SL}_2(\mathbb{Z})$. Homological Broadhurst–…

Let $L$ be a Lie algebra with a group grading $\Gamma$ that is a coarsening of an abelian grading of $L$. Abelianness conjecture. Then $\Gamma$ is abelian. The paper states that no…

Let $\operatorname{Gr}\operatorname{IA}_n$ be the graded Lie algebra associated to the Andreadakis filtration of $\operatorname{IA}_n$. The stable Lie-algebra comparison conjecture…

Let $G$ be the connected reductive group with involution $\theta$, let $K=G^\theta$, and let $\mathfrak g_1$ be the degree-one component of the associated graded Lie algebra. Write…

Let $G$ be the connected reductive group with involution $\theta$, let $K=G^\theta$, and let $\mathfrak g_1$ be the degree-one component of the associated graded Lie algebra. For a…

Vilonen–Xue conjecture. The character sheaves constructed in this paper, together with those constructed in the earlier work, constitute all cuspidal character sheaves for graded c…

Let ${\mathfrak{g}}_1$ be the degree-one component of one of the stably graded Lie algebras considered here, let $K$ act on ${\mathfrak{g}}_1$, and let ${\mathfrak{g}}_1^{rs}$ be i…

Let ${\mathfrak{g}}_1$ be the degree-one component of a stably graded Lie algebra, let $K$ act on ${\mathfrak{g}}_1$, and let $\chi$ be a character indexing the nearby-cycle sheaf…

Let $\mathfrak{m}=\bigoplus_{i<0}\mathfrak{m}_i$ be a fundamental graded nilpotent Lie algebra, and let…