Abstract

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 = 𝔾m reduces to the classical Birch–Tate conjecture.

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