Local-to-global extensions for wildly ramified covers of curves

Mardi 8 octobre 11:00-12:15 - Renee Bell - IMO et Université de Pennsylvanie

Résumé : Given a Galois cover of curves X —> Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series rings k((u))/k((t)). If we fix a base curve Y, we can ask when a Galois extension of Laurent series rings comes from a global cover of Y in this way. Harbater proved that over a separably closed field, every Laurent series extension comes from a global cover for any base curve if G is a p-group, and he gave a condition for the uniqueness of such an extension. Using a generalization of Artin-Schreier theory to non-abelian p-groups, we fully characterize the curves Y for which this extension property holds and for which it is unique up to isomorphism, but over a more general ground field.

Lieu : salle 3L08 bâtiment 307

Local-to-global extensions for wildly ramified covers of curves  Version PDF