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Unramified Geometric Iwasawa theory of function fields
Abstract
For an algebraically closed field k of characteristic p>0, we study unramified Zp-towers {Xn}n≥ 0 of smooth, projective and connected curves over k. Our main result provides an Iwasawa-theoretic description of the Newton polygons of their Jacobians, establishing that the slopes of the new part at level n are eventually affine functions of p−n with rational coefficients.
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BibTeX
@misc{cais2026unramified,
title = {{Unramified Geometric Iwasawa theory of function fields}},
author = {Bryden Cais and Daniel Lewis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17975},
eprint = {2609.17975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17975},
}
RIS
TY - UNPB
TI - Unramified Geometric Iwasawa theory of function fields
AU - Bryden Cais
AU - Daniel Lewis
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.17975
UR - https://arxiv.org/abs/2609.17975
AB - For an algebraically closed field k of characteristic p>0, we study unramified Z_p-towers {X_n}_n≥ 0 of smooth, projective and connected curves over k. Our main result provides an Iwasawa-theoretic description of the Newton polygons of their Jacobians, establishing that the slopes of the new part at level n are eventually affine functions of p^−n with rational coefficients.
ER -