5 problems

Let $K$ be a number field and let $Z/K$ be a smooth projective irreducible variety of dimension $d$. Define the Albanese kernel by … Here $\mathrm{CH}^d(Z)_0$ is the group of homol…

Let $K$ be a global field, let $Y$ be a smooth projective variety over $K$, and let $i\in\mathbb{Z}$. Write $\operatorname{CH}^i(Y)_0$ for the kernel of the cycle class map and let…

Let $Y$ be a smooth projective variety over a global field, and let $i\in\mathbb{Z}$. Write $\operatorname{CH}^i(Y)_0$ for the kernel of the cycle class map on…

Let $E/F$ be a CM extension of number fields, with complex conjugation $\mathtt{c}$, and let $n=2r$ be an even positive integer. Let $W_r=E^n$ with the specified skew-hermitian for…

Let $E$ be a number field, let $f$ be the modular form under consideration, let $L(f\otimes E,s)$ be its complex $L$-function over $E$, and let $X_\mathfrak{p}(E)$ be the associate…