5 problems

Algebraicity conjecture for Lefschetz operators. The operator $\Lambda$ is induced by an operator of the form $I_{\operatorname{H}}(Z)$ for some closed sub-scheme…

Let $\gamma$ be an algebraic cycle, and let $\operatorname{cl}(\gamma)$ denote its cohomology class under a Weil cohomology theory. Grothendieck's standard conjecture. If $\gamma$…

Grothendieck's standard conjectures. The following assertions hold: (1) there exist correspondences $\Lambda_j\in CH^j(Y\times Y)$ such that $\Lambda_{j*}:H^{2d_Y-j}(Y)\to H^j(Y)$…

Let $V$ be a variety equipped with a standard Weil cohomology theory. Two algebraic cycles are numerically equivalent when they have the same intersection numbers with all cycles o…

Let $k$ be an algebraically closed field, let $H_W$ be a Weil cohomology theory on varieties over $k$, and let $X$ be a variety of dimension $d$. Let $\mathcal{A}_W^r(X)$ be the…