English

Linking Numbers and the Tame Fontaine-Mazur Conjecture

Number Theory 2013-08-28 v1

Abstract

Let p be an odd prime, let S be a finite set of primes q congruent to 1 mod p but not mod p^2 and let G_S be the Galois group of the maximal p-extension of Q un-ramified outside of S. If r is a continuous homomorphism of G_S into GL_2(Z_p) then under certain conditions on the linking numbers of S we show that r=1 if its reduction mod p is 1. We also show that the reduction of r mod p is 1 if r can be put in triangular form mod p^3.

Keywords

Cite

@article{arxiv.1308.5920,
  title  = {Linking Numbers and the Tame Fontaine-Mazur Conjecture},
  author = {John Labute},
  journal= {arXiv preprint arXiv:1308.5920},
  year   = {2013}
}