On the asymptotics of elementary-abelian extensions of local and global function fields
N. Potthast, Transactions of the American Mathematical Society 379 (2026) 289–340.
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Abstract
<p>We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p">
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<mml:mi>p</mml:mi>
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</inline-formula>. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.</p>
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Journal Title
Transactions of the American Mathematical Society
Volume
379
Issue
1
Page
289 - 340
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Potthast N. On the asymptotics of elementary-abelian extensions of local and global function fields. Transactions of the American Mathematical Society. 2026;379(1):289-340. doi:10.1090/tran/9509
Potthast, N. (2026). On the asymptotics of elementary-abelian extensions of local and global function fields. Transactions of the American Mathematical Society, 379(1), 289–340. https://doi.org/10.1090/tran/9509
@article{Potthast_2026, title={On the asymptotics of elementary-abelian extensions of local and global function fields}, volume={379}, DOI={10.1090/tran/9509}, number={1}, journal={Transactions of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Potthast, Nicolas}, year={2026}, pages={289–340} }
Potthast, Nicolas. “On the Asymptotics of Elementary-Abelian Extensions of Local and Global Function Fields.” Transactions of the American Mathematical Society 379, no. 1 (2026): 289–340. https://doi.org/10.1090/tran/9509.
N. Potthast, “On the asymptotics of elementary-abelian extensions of local and global function fields,” Transactions of the American Mathematical Society, vol. 379, no. 1, pp. 289–340, 2026, doi: 10.1090/tran/9509.
Potthast, Nicolas. “On the Asymptotics of Elementary-Abelian Extensions of Local and Global Function Fields.” Transactions of the American Mathematical Society, vol. 379, no. 1, American Mathematical Society (AMS), 2026, pp. 289–340, doi:10.1090/tran/9509.
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