9 problems

Let $S$ be a regular scheme of dimension $1$, let $f:X\to S$ be projective and flat with $X$ regular of dimension $n+1$, and let $\widehat{\operatorname{Ch}}^i(X)$ be the modified…

Let $X$ be a regular, projective, flat scheme over $\operatorname{Spec}\mathbb Z$ of absolute dimension $d+1$, and let $\overline{M}$ be an arithmetically ample hermitian line bund…

Arithmetic analogues of Grothendieck's standard conjectures. For a suitable choice of $k$, if $2p\leq d+1$, then (a) the homomorphism

Let $X$ be the regular arithmetic or geometric variety in the paper, let $\overline{\operatorname{Ch}}^1(X)$ and $\overline{\operatorname{Ch}}^n(X)$ be the admissible Arakelov Chow…

Let $K$ be a finite Galois extension of $\mathbb Q$. Assume that every embedding of $K$ into $\mathbb C$ factors through an embedding of ${\rm Frac}(D)$ into $\mathbb C$, that the…

Assume the hypotheses of the Gross–Deligne-type conjecture for the abelian scheme $f:{\cal A}\to Y$, including the $\mathcal O_K$-action, the parity condition on $\chi$ and $l$, an…

Let $K$ be a finite Galois extension of $\mathbb Q$ and let $c$ be a central element of ${\rm Gal}(K/\mathbb Q)$ inducing complex conjugation under every embedding. Assume that all…

Let $f:X\rightarrow Y$ be a $\mu_n$-equivariant smooth and projective morphism of equivariant regular arithmetic varieties, with trivial $\mu_n$-action on $Y$. Let $\chi$ be a Diri…

Let $X$ be a regular scheme that is projective and flat over $\mathbb Z$, and let $\widehat{\operatorname{CH}}^m(X)_{\mathbb R}$ denote its arithmetic Chow group. The Gillet–Soulé…