| Autor: |
Booher, Jeremy, Cais, Bryden |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Alg. Number Th. 14 (2020) 587-641 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.2140/ant.2020.14.593 |
| Popis: |
Let $\pi : Y \to X$ be a branched $\mathbf{Z}/p \mathbf{Z}$-cover of smooth, projective, geometrically connected curves over a perfect field of characteristic $p>0$. We investigate the relationship between the $a$-numbers of $Y$ and $X$ and the ramification of the map $\pi$. This is analogous to the relationship between the genus (respectively $p$-rank) of $Y$ and $X$ given the Riemann-Hurwitz (respectively Deuring--Shafarevich) formula. Except in special situations, the $a$-number of $Y$ is not determined by the $a$-number of $X$ and the ramification of the cover, so we instead give bounds on the $a$-number of $Y$. We provide examples showing our bounds are sharp. The bounds come from a detailed analysis of the kernel of the Cartier operator. |
| Databáze: |
arXiv |
| Externí odkaz: |
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