4 problems

Let $X$ be a smooth projective variety of dimension $m$, let ${\mathbb F}$ be the coefficient field used in the source, and let $\widetilde{L}^tH^k(X;{\mathbb F})$ be the image of…

Let $g_c:\mathbb T^n\to\mathbb T^n$ be a continuous map whose induced map on first homology has characteristic polynomial $t^n-c$, where $c>2$ and $n>1$ is a positive integer. Writ…

Let $X$ be a smooth projective variety over an algebraically closed field $K$ of dimension $n$. For an integer $i$, let ${\mathrm{Ch}}^i(X)$ be the group of Chow cycles of codimens…

Let $X$ be a smooth projective variety of dimension $n$, let $h$ be a hyperplane section, and let $L$ be the Lefschetz operator induced by intersecting with $h$. Thus … is an isomo…