Potential automorphy for $$GL_n$$

Rigid Local Systems and Potential Automorphy: the G 2 -case

For s ∈ P(Q) \ {0, 1}, we study the compatible system of Galois representations (ρ l (3) : Gal(Q̄/Q) → G2(Ql))l introduced in [4], where G2(Ql) ≤ GL7(Ql) is the simple group of type G2. We prove that, under some mild condition on s, the image of the Tate twisted Galois representation ρ l (3) coincides with G2(Zl) for all l up to a set of primes having density zero, and we show that ρ l is potent...

Potential Automorphy of Odd-dimensional Symmetric Powers of Elliptic Curves, and Applications

The present article was motivated by a question raised independently by Barry Mazur and Nick Katz. The articles [CHT,HST,T] contain a proof of the Sato-Tate conjecture for an elliptic curve E over a totally real field whose j-invariant j(E) is not an algebraic integer. The Sato-Tate conjecture for E is an assertion about the equidistribution of Frobenius angles of E, or equivalently about the n...

AUTOMORPHY FOR SOME l-ADIC LIFTS OF AUTOMORPHIC

We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spi...

an appropriate model for exchange rate predictability in iran: comparing potential forecastability

nowadays in trade and economic issues, prediction is proposed as the most important branch of science. existence of effective variables, caused various sectors of the economic and business executives to prefer having mechanisms which can be used in their decisions. in recent years, several advances have led to various challenges in the science of forecasting. economical managers in various fi...

Automorphy for some l-adic lifts of automorphic modl Galois representations. II