Un critère d'épointage des sections l-adiques

2012/01/22 by Niels Borne, Borne, Niels, Michel Emsalem +1
Mathematics · #14G05 #14H30 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:14G05 #msc:14H30

paper · pdf · doi:10.48550/arxiv.1201.4589

20 pages, in French. Some corrections, new Lemme 9

arxiv created 2013/01/21 · arxiv updated 2013/01/22

Abstract

The cuspidalization conjecture emerged as an approach of Grothendieck's famous section conjecture. We address a weak form of it by using a mild generalization of a theorem of Uwe Jannsen which describes exactly when the l-adic homology of an open curve is a pure Galois representation. We also give some concrete examples of modular curves for which the cuspidalization is possible at the l-adic level.

Related

• Arithmetic in the fundamental group of a p-adic curve: On the p-adic section conjecture for curves
• Birational p-adic Galois sections in higher dimensions
• Local sections of arithmetic fundamental groups of p-adic curves
• Cusps and q-expansion principles for modular curves at infinite level
• Galois sections and p-adic period mappings