Related papers: Galois representations attached to automorphic for…

We introduce the notion of finite slope families to encode the local properties of the p-adic families of Galois representations appearing in the work of Harris, Lan, Taylor and Thorne on the construction of Galois representations for…

We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group $GSp_6$ compatible when one varies the level at $p$. These classes are expected constituents of an Euler system for the…

We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps…

The study of modular representation theory of the double covering groups of the symmetric and alternating groups reveals rich and subtle combinatorial and algebraic phenomena involving their irreducible characters and the structure of their…

We introduce an $A_\infty$-algebra structure on the Hochschild cohomology of the endomorphism bimodule of a finite-dimensional representation of an associative algebra. We prove that this structure determines a presentation for…

We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual…

We prove exceptional zero conjectures for $p$-ordinary regular algebraic cuspidal automorphic representations of $\mathrm{GL}_3(\mathbb{A})$ which are Steinberg at $p$. We make no self-duality assumptions. The paper has two parts. In Part…

In this paper we study the compatible family of degree-4 Scholl representations $\rho_{\ell}$ associated with a space $S$ of weight $\kappa> 2$ noncongruence cusp forms satisfying Quaternion Multiplications over a biquadratic field $K$. It…

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into…

Given a compatible system of n-dimension l-adic Galois representations arising from \'etale cohomology of any complete, non-singular variety, we prove that for sufficiently large prime l, type A Galois image (in the Cartan-Killing…

Let $\tau_1^{(r)}$, $\tau_2^{(r)}$ be two genuine cuspidal automorphic representations on $r$-fold covers of the adelic points of the general linear groups $GL_{n_1}$, $GL_{n_2}$, resp., and let $E(g,s)$ be the associated Eisenstein series…

We use Galois cohomology methods to produce optimal mod $p^d$ level lowering congruences to a $p$-adic Galois representation that we construct as a well chosen lift of a given residual mod $p$ representation. Using our explicit Galois…

We study the residual monodromy representations associated to the Dwork family in characteristic two. Various applications involving 2-adic and mod 2 Galois representations are discussed. Combining the author's previous work with Tsuzuki…

The group $\GL_2$ over a local field with (residue) characteristic $2$ possesses much more smooth supercuspidal $\ell$-adic representations, than over a local field of residue characteristic $> 2$. One way to construct these representations…

Let $F$ be a CM field and let $(\overline{r}_{\pi,\lambda})_{\lambda}$ be the compatible system of residual $\mathcal{G}_n$-valued representations of $\operatorname{Gal}_{F}$ attached to a RACSDC automorphic representation $\pi$ of…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$, and let $\sigma$ denote its non-trivial automorphism. Let $R$ be an algebraically closed field of characteristic different…

Let $X$ be a smooth, projective, geometrically connected curve over a finite field $\mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Its dual group $\hat{G}$ is a split reductive group over $\mathbb{Z}$.…

The global deformation theory of residually reducible Galois representations with fixed auxiliary conditions is studied. We show that $\bar{\rho}:\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow…

We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…

We remove a parity condition from the construction of automorphic Galois representations carried out in the Paris Book Project. We subsequently generalize this construction to the case of `mixed-parity' (but still regular essentially…