Newton Polygons of Artin-Schreier Coverings Curves

Abstract: Let $X$ be a smooth, affine, geometrically connected curve over a finite field of characteristic $p > 2$. Let $C/X$ be a finite Galois covering of degree p. A theorem of Kramer-Miller states that the p-adic Newton polygon NP($C$) is bounded below by a certain Hodge polygon HP($C$) which is defined in terms of local monodromy invariants of $C/X$. Our main result is a local criterion that is necessary and sufficient for NP($C$) and HP($C$) to coincide. Time permitting, we will discuss some further results concerning the interaction of these two polygons. This is joint work with Joe Kramer-Miller.

number theory

Audience: researchers in the discipline

Comments: Register for the next session of NDNT Round 5 on February 15 using the following links:

uwmadison.zoom.us/meeting/register/tJMkc-2hqDojG9yua5n-EkWxonnHyGeeMJkJ

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POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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