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Deformations for Function Fields

✍ Scribed by David T Ose

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 360 KB
Volume: 70
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2224

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✦ Synopsis

We consider a question of describing the one-dimensional P-adic representations that lift a given representation over a finite field of the absolute Galois group of a function field. In this case, the characterization of abelian p-power extensions of fields of characteristic p can be extended to abelian pro-p-extensions, and refined to allow only restricted ramification at the places of K, and can be a tool for analyzing one-dimension P-adic representations. We then turn to the problem of classifying those representations which can be realized as the action of the Galois group on the division points of a rank one Drinfeld module, discussing both results and a conjecture about the form of the representations that arise in this manner.

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