Milnor $K$-group attached to a torus and Birch-Tate conjecture

Details Milnor $K$-group attached to a torus and Birch-Tate conjecture Milnor $K$-group attached to a torus and Birch-Tate conjecture

2008-04-21

arxiv.org/abs/0804.3260v1

Mathematics

Number Theory

16 pages

Scientific paper

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.

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