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I'm not an expert in local cohomology, but the following problems have come up in my work, and I'd like to get a sense of where things stand. Let $\mathbb{A}^n=\operatorname{Spec} \mathbb{C}[x_1, \dot …

When dealing with affine Kac-Moody groups, especially geometrically (e.g. by examining their affine flag varieties or affine Grassmannians) I've been taught that time and time again, issues arise in t …

I believe this is addressed on page 52, underneath the statement of Iwahori's theorem. He provides an argument for why Iwahori's result can be strengthened to G reductive by considering $G \rightarrow …

I'm interested in the intersection homology of toric varieties associated to a polytope $P$ with proper faces F, and a subdivision $P'$ of P. Let $X_P$ be the toric variety associated to the polytope …

I have a collection of related (to me) questions, which stem from the fact that I feel like I have a bunch of pieces, but not a full clear picture. I'm curious about forms of reductive groups in gener …

I've got a couple rather geometric questions about the following setup. Let $X$ be a scheme over an algebraically closed field ($\mathbb{C}$, say) with the action of a torus $T$, such that the action …

I've spent lots of time in Chriss and Ginzburg's "Complex Geometry and Representation Theory" and despite convolution (in Borel-Moore homology or K-theory) being very central, I feel like I'm still la …

I'll write the two lemmas I have questions about, and then ask my questions. For reference, I'm using the following definition of Gorenstein: $\mathbf{Definition\ 1.15}$ A local noetherian ring $A$ i …