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I was going to write this as a comment, but it turned out too long so I am posting it as an answer. The Kontsevich-Zagier periods include periods of motives over $\overline{\mathbb{Q}}$ (well at least …

As the title suggests, the question is about products of subgroups of a unipotent algebraic group. I will work with max-spec for algebraic groups over fields, and given an algebraic group $G$, by writ …

Let $X$ be a smooth projective curve of genus $\geq 1$ over $\mathbb{C}$, $H^\cdot=H^\cdot(X)$, and $K$ be the kernel of cup product $\cup: H^1\otimes H^1\rightarrow H^2$. Consider the extension of Ho …

Suppose $f:X\longrightarrow Y$ is a surjective morphism of smooth complex varieties. Let $S$ be a subset of $X(\mathbb{C})$. I'm wondering if there are results that roughly say that if the intersectio …

Suppose $Y$ is a smooth projective variety of dimension $2p-1$ over $\mathbb{C}$. I have a few questions about the $p^{~\text{ th}}$ intermediate Jacobian $J^p(Y)$ of $Y$. Does it come from (i.e. is …

More precisely, let $G$ be an affine group scheme over a field $k$, $Rep_k(G)$ be the category of finite dimensional representations of G, and $\omega_0$ be the forgetful functor from $Rep_k(G)$ to th …