4 research outputs found
Even Galois Representations and the Fontaine--Mazur conjecture II
We prove, under mild hypotheses, that there are no irreducible
two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de
Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis
required in previous work of the author. We construct examples of irreducible
two-dimensional residual representations that have no characteristic zero
geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main
theorems remain unchange
Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane
The distribution of auxiliary primes raising the level of even
representations of tetrahedral type is studied. Under an equidistribution
assumption, the density of primes raising the level of an even, -adic
representation is shown to be Data on auxiliary primes
raising the level of even -adic representations of various
conductors are presented. The data support equidistribution for . In the
process, we prove existence of even, surjective representations ramified only at
and at for and . The prime falls
outside the class of Shanks primes. Measured by conductor, these are the
smallest known examples of totally real extensions of with Galois
group .Comment: 22 pages, 4 tables, 1 figure. arXiv admin note: text overlap with
arXiv:2309.0187