Papers › An Infinite Family of Artin-Schreier Curves with Minimal a-number
An Infinite Family of Artin-Schreier Curves with Minimal a-number
Iris Y. Shi
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Let p be an odd prime and k be an algebraically closed field with characteristic p. Booher and Cais showed that the a-number of a ℤ/p ℤ-Galois cover of curves ϕ: Y →X must be greater than a lower bound determined by the ramification of ϕ. In this paper, we provide evidence that the lower bound is optimal by finding examples of Artin-Schreier curves that have a-number equal to its lower bound for all p. Furthermore we use formal patching to generate infinite families of Artin-Schreier curves with a-number equal to the lower bound in any characteristic.
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