Mathematical Research Letters

Volume 20 (2013)

Number 5

On $p$-adic periods for mixed Tate motives over a number field

Pages: 825 – 844



Andre Chatzistamatiou (Fachbereich Mathematik, Universität Duisburg-Essen, Essen, Germany)

Sinan Ünver (Mathematics Department, Koç University, Istanbul, Turkey)


For a number field, we have a Tannaka category of mixed Tate motives at our disposal. We construct $p$-adic points of the associated Tannaka group by using $p$-adic Hodge theory. Extensions of two Tate objects yield functions on the Tannaka group, and we show that evaluation at our p-adic points is essentially given by the inverse of the Bloch-Kato exponential map.

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