4 problems

Permissible-polynomial conjecture. Every permissible polynomial is a Chinburg polynomial, with the displayed linear combination determined by its $(f_1,\ldots,f_s)$-permissibility.…

Chinburg's conjectures. For every fundamental discriminant $-f<0$, there exists a bivariate rational function $P\in\mathbf{Z}(x,y)$ and a rational number $r\in\mathbf{Q}^{\times}$…

Mixed linear independence conjecture. As ${\mathbb Q}$-subspaces of ${\mathbb R}$,

Beilinson's linear independence conjecture. The values $L^{(N)'}(-1,x)$, for $x\in U$, are linearly independent over ${\mathbb Q}$. This is presented as a consequence of the Beilin…