2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159239We formulate (and prove under a certain assumption) a conjecture relating the order of Somekawa's Milnor $K$-group attached to a torus $T$ and the value of the Artin $L$-function attached to the cocharacter group of $T$ (regarded as an Artin representation) at $s=-1$. The case $T=\G_m$ reduces to the classical Birch-Tate conjecture.16 pagesNumber TheoryK-Theory and Homology11R70 (Primary); 11R42, 19F15 (Secondary)text