6 problems

Let $F$ be a subfield of $\mathbb{C}$ with embedding $\sigma:F\hookrightarrow\mathbb{C}$. Let $\mathcal B(F)$ and $\mathcal B(\mathbb{C})$ denote the corresponding Bloch groups, an…

Let $X$ be a smooth, projective scheme over ${\cal O}_K[1/S]$, and let $\bar{X}:=X\times_{{\cal O}_K[1/S]}\bar{K}$ be its base change to an algebraic closure. For integers $i$ and…

Goncharov's regulator image conjecture. The image of this regulator map in Deligne cohomology coincides with the image of Beilinson's regulator map.

Let $X$ be a smooth, projective, geometrically connected curve of genus $g$ defined over $\mathbb{Q}$. Let $K_4^{(3)}(X)$ denote the third Adams eigenspace of…

Let $A^j_{\eta}$ be the $j$-fold power of the universal elliptic-curve family over the generic point $\eta$, and let…

Let $\mathbb L(F)$ be the Lie coalgebra of multiple polylogarithms over a field $F$, with cobracket $\delta$, and let $\mathbb L^{\operatorname{symb}}(\mathbb C)$ be its symbolic v…