p-adic heights and Vologodsky integration

2017/11/19 by Besser, Amnon
#11G20 #11S25 (Secondary) #11S80 #14F40 #14G40 (Primary) 14G22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1711.06957

Abstract

We extend the result of a previous work to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a p-adic height pairing. we show that this pairing still equals the one defined by Nekovar.

Related

• The p-adic height pairings of Coleman-Gross and of Nekovar
• Coleman-Gross height pairings and the p-adic sigma function
• Computing local p-adic height pairings on hyperelliptic curves
• Computing p-adic heights on hyperelliptic curves
• Vologodsky integration on curves with semi-stable reduction