Canonical factorization of morphisms of Berkovich curves

Vendredi, 3. mai 2019 - 14:00 - 15:00
Orateur: 

Velibor Bojkovic (LMNO)

Résumé: 

After revising a large class of extensions of valued fields for which one has sensible ramification theory and Herbrand function, we prove that such extensions decompose into canonical towers whose intermediate extensions have particularly simple Herbrand function. In the latter part we will focus on applying such factorizations to geometric settings of nonarchimedean geometry and Berkovich curves (deducing some harmonicity properties for finite morphisms of such curves). 

A more transparent example/consequence is that given an analytic function on a unit disc over a complete, non-archimedean algebraically closed field of mixed characteristic, then under certain (natural) conditions it can be factorized as a product of analytic functions whose valuation polygons have only break point.