A Herbrand-Ribet theorem for function fields

Details A Herbrand-Ribet theorem for function fields A Herbrand-Ribet theorem for function fields

2011-04-28

arxiv.org/abs/1104.5363v3

Mathematics

Number Theory

to appear in Inventiones Mathematicae

Scientific paper

10.1007/s00222-011-0346-3

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 $\mu_p$-coefficients over the splitting field of $\mu_p$, and in our analogue both occurrences of $\mu_p$ 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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