Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)

Details Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong) Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)

2003-12-29

arxiv.org/abs/math/0312490v2

Mathematics

Number Theory

This revised version is cleaner, although not substantially different. We check that our arguments work for \ell=2

Scientific paper

As a sequel to our proof of the analog of Serre's conjecture for function fields in Part I of this work, we study in this paper the deformation rings of $n$-dimensional mod $\ell$ representations $\rho$ of the arithmetic fundamental group $\pi_1(X)$ where $X$ is a geometrically irreducible, smooth curve over a finite field $k$ of characteristic $p$ ($\neq \ell$). We are able to show in many cases that the resulting rings are finite flat over $\BZ_\ell$. The proof principally uses a lifting result of the authors in Part I of this two-part work, Taylor-Wiles systems and the result of Lafforgue. This implies a conjecture of A.J. ~de Jong for representations with coefficients in power series rings over finite fields of characteristic $\ell$, that have this mod $\ell$ representation as their reduction.

Affiliated with

Also associated with

No associations

Rating

Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-600110