Surjectivity of $p$-adic regulator on $K_2$ of Tate curves

Details Surjectivity of $p$-adic regulator on $K_2$ of Tate curves Surjectivity of $p$-adic regulator on $K_2$ of Tate curves

2005-02-10

arxiv.org/abs/math/0502222v3

Mathematics

Number Theory

Scientific paper

10.1007/s00222-005-0494-4

I prove the surjectivity of the $p$-adic regulator from Quillen's $K_2$ of
Tate curve to the $p$-adic etale cohomology group when the base field is
contained in a cyclotomic extension of $Q_p$. This implies the finiteness of
torsion part of $K_1$ of Tate curves thanks to Suslin's exact sequence.

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