We 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.
Iwasawa Theory for Artin Representations, I
On characteristic ideal of Selmer group associated to Artin representations
Artin representations for GSp_4 attached to real analytic Siegel cusp forms of weight (2,1)
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