Abstract
We prove a function field analogue of the Herbrand-Ribet theorem on cyclotomic number fields. The Herbrand-Ribet theorem can be interpreted as a result about cohomology with μ p -coefficients over the splitting field of μ p , and in our analogue both occurrences of μ p are replaced with the \(\mathfrak{p}\)-torsion scheme of the Carlitz module for a prime \(\mathfrak{p}\) in F q [t].
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Taelman, L. A Herbrand-Ribet theorem for function fields. Invent. math. 188, 253–275 (2012). https://doi.org/10.1007/s00222-011-0346-3
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DOI: https://doi.org/10.1007/s00222-011-0346-3