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Stark units in positive characteristic
Author(s) -
Anglès Bruno,
Ngo Dac Tuan,
Tavares Ribeiro Floric
Publication year - 2017
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12051
Subject(s) - mathematics , rank (graph theory) , equivariant map , sign (mathematics) , class (philosophy) , pure mathematics , series (stratigraphy) , combinatorics , discrete mathematics , mathematical analysis , paleontology , artificial intelligence , computer science , biology
We show that the module of Stark units associated to a sign‐normalized rank one Drinfeld module can be obtained from Anderson's equivariant A ‐harmonic series. We apply this to obtain a class formula à la Taelman and to prove a several variable log‐algebraicity theorem, generalizing Anderson's log‐algebraicity theorem. We also give another proof of Anderson's log‐algebraicity theorem using shtukas and obtain various results concerning the module of Stark units for Drinfeld modules of arbitrary rank.