8 problems

A generalized affine Springer fiber is the variety associated with a reductive group, a finite-dimensional representation, and an element of the corresponding loop-space representa…

Let $Y$ be the additive character variety associated to a reductive group $G$, a genus $g$, and a tuple of $G$-orbits in the Lie algebra, under the additive genericity assumptions.…

Let $k$ be a field, let $G$ be a connected reductive group over $k$, and let $X$ be an irreducible smooth $k$-scheme with function field $K$. Purity for $G$-torsors over $X$ means…

Fundamental-domain purity conjecture. The cohomology of $F_{\gamma}$ is pure in the sense of Deligne.

Let $k$ be the ground field, let $G$ be a non-special semisimple $k$-group scheme, and let $X$ be a smooth affine $k$-variety. Purity failure conjecture. There exists a smooth affi…

Let $C$ be a projective geometrically integral algebraic curve over $k$ whose singularities are all planar, and let $\overline{\operatorname{Jac}}_{C}$ be its compactified Jacobian…

Let $F_{\gamma}$ be the fundamental domain for the action of the free abelian group generated by $\chi(\epsilon)$, with $\chi\in X_{*}(T)$, on the affine Springer fiber…

Let $k=\mathbf{F}_{q}$, let $G$ be a connected reductive group split over $k$, and let $\gamma\in \mathfrak{t}(\mathcal{O})$ be regular, with affine Springer fiber … Here…