Geodesic
Prolongations of $t$-Motives and Algebraic Independence of Periods
Documenta mathematica, Tome 23 (2018), pp. 815-838.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this article we show that the coordinates of a period lattice generator of the $n$-th tensor power of the Carlitz module are algebraically independent, if $n$ is prime to the characteristic. The main part of the paper, however, is devoted to a general construction for $t$-motives which we call prolongation, and which gives the necessary background for our proof of the algebraic independence. Another incredient is a theorem which shows hypertranscendence for the Anderson-Thakur function $\omega(t)$, i.e. that $\omega(t)$ and all its hyperderivatives with respect to $t$ are algebraically independent.
Classification : 11J93, 11G09, 13N99
Keywords: Drinfeld modules, $t$-modules, transcendence, higher derivations, hyperdifferentials 
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     author = {Maurischat, Andreas},
     title = {Prolongations of $t${-Motives} and {Algebraic} {Independence} of {Periods}},
     journal = {Documenta mathematica},
     pages = {815--838},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a37/}
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Maurischat, Andreas. Prolongations of $t$-Motives and Algebraic Independence of Periods. Documenta mathematica, Tome 23 (2018), pp. 815-838. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a37/