The decomposition law over the compositum of Artin-Schreier extensions

Let K be a function field over a perfect constant field of positive characteristic p, and L the compositum field of some (degree p) Artin-Schreier extensions of K. We study how places of K split in this elementary abelian p-extension L/K. One consequence of our results is that the negation of Abyankar's Lemma is true whenever the (tamely ramified) assumption of Abyankar's Lemma is violated. It turns out that a place of K totally ramifies in L/K (is inert, splits completely, resp.) if and only if it totally ramifies (is inert, splits completely, resp.) in all of the intermediate degree p Artin-Schreier extensions over K. Examples are given to show that all theoretically possible decomposition laws are indeed possible. These examples are independent of the function field structure of K and its characteristic p.

Note: There will be no prerequisite requirements to understand the talk, though familiarity with algebraic number theory will help.

(This is joint work with R. Scheidler)