Relations Between Multizeta Values for $\mathbb F_q[t]$

Despite the failure of naive analogs of the sum shuffle or integral shuffle relations, and despite the lack of understanding of analogs of many classical structures that exist in the corresponding theory in the number field case, the multizeta values defined by the author are proved (and conjectured) to satisfy many interesting and combinatorially involved identities. The connections of these multizeta values with iterated extensions of Carlitz–Tate t-motives, analogs of Ihara power series, and Deligne–Soulé cocycles, etc., make it an interesting challenge to understand all the identities and discover the other relevant underlying structures.