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

TL;DR

This paper constructs p-adic points of the Tannaka group for mixed Tate motives over a number field using p-adic Hodge theory, linking extensions of Tate objects to the Bloch-Kato exponential map.

Contribution

It introduces a method to construct p-adic points of the Tannaka group via p-adic Hodge theory, connecting extensions of Tate objects to the Bloch-Kato exponential.

Findings

Construction of p-adic points of the Tannaka group.

Evaluation at these points relates to the inverse Bloch-Kato exponential.

Provides new tools for studying mixed Tate motives over number fields.

Abstract

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.