Abstract
In this chapter we establish the connection between the spaces used to represent the Frobenius endomorphism, and eigenspaces for a Galois group of automorphisms of the Artin-Schreier curve. This connects Dwork theory, the Washnitzer-Monsky theory, and the fact realized by Monsky that the series EĎ€(x) can be used to construct explicitly such eigenspaces. The first section lays the foundations for the special type of ring under consideration. After that we study the Artin-Schreier equation and the Frobenius endomorphism.
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© 1990 Springer Science+Business Media New York
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Lang, S. (1990). Gauss Sums and the Artin-Schreier Curve. In: Cyclotomic Fields I and II. Graduate Texts in Mathematics, vol 121. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0987-4_16
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DOI: https://doi.org/10.1007/978-1-4612-0987-4_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6972-4
Online ISBN: 978-1-4612-0987-4
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