Generalized logarithmic derivatives for K_n

2006/11/06 by Sarah Livia Zerbes, Zerbes, Sarah Livia
Mathematics · #11R23 #11S70 #19F99 #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11R23 #msc:11S70 #msc:19F99

paper · pdf · doi:10.48550/arxiv.math/0611136

34 pages

arxiv created 2006/11/06 · openalex publication_date 2006/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct (generalized) logarithmic derivatives for general n-dimensional local fields K of mixed characteristics (0,p) in which p is not necessarily a prime element with residue field k such that [k:k^p]=p^n-1. For the construction of the logarithmic derivative map, we define n-dimensional rings of overconvergent series and show that - as in the 1-dimensional case - they can be interpreted as functions converging on some annulus of the open unit p-adic disc. Using the generalized logarithmic derivative, we give a new construction of Kato's n-dimensional dual exponential map.

Related

• On logarithmic derivatives of zeta functions in families of global fields
• Conjectures on the logarithmic derivatives of Artin L-functions II
• An explicit André-Oort type result for P¹(C) x G_m(C) based on logarithmic forms
• GENERALIZED LOGARITHMIC DERIVATIVE ESTIMATES OF GOL'DBERG–GRINSHTEIN TYPE
• Logarithmic differentials on discretely ringed adic spaces