Geodesic
Prolongations of $t$-Motives and Algebraic Independence of Periods
Documenta mathematica, Tome 23 (2018), pp. 815-838
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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 ω(t), i.e. that ω(t) and all its hyperderivatives with respect to t are algebraically independent.
DOI : 10.4171/dm/635
Classification : 11G09, 11J93, 13N99
Mots-clés : Drinfeld modules, transcendence, t-modules, higher derivations, hyperdifferentials 
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     author = {Andreas Maurischat},
     title = {Prolongations of $t${-Motives} and {Algebraic} {Independence} of {Periods}},
     journal = {Documenta mathematica},
     pages = {815--838},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/635},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/635/}
}
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Andreas Maurischat. Prolongations of $t$-Motives and Algebraic Independence of Periods. Documenta mathematica, Tome 23 (2018), pp. 815-838. doi: 10.4171/dm/635

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