Mathematical Research Letters
Volume 20 (2013)
On $p$-adic periods for mixed Tate motives over a number field
Pages: 825 – 844
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.