Mixed Carlitz Motives And Colored Multizeta Values In Characteristic P

This thesis studies characteristic p multizeta values, which are function field analogs of the Euler-Riemann multizeta values. The objective of this thesis is two-fold. We first explicitly construct the category of mixed Carlitz motives, which is a counterpart to the category of mixed Tate motives in characteristic zero. After that, we identify specific mixed Carlitz motives, and use them to derive algebraic independence properties of colored multizeta values. The former includes all known t-motives related to multizeta values, while the latter complements results in the literature on algebraic relations between multizeta values.