相关论文: On the rationality of algebraic monodromy groups o…

Let $X$ be a normal geometrically connected variety over a finite field $\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups…

Let $X$ be a complete smooth variety defined over number field $K$ and $i$ an integer. The absolute Galois group of $K$ acts on the $i$th $l$-adic etale cohomology of $X$ for all $l$, producing a system of $l$-adic representations…

Let K be a number field and {V_l} be a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let G_l and V_l^ab be respectively the algebraic monodromy group and the maximal abelian…

Let $\{\rho_\lambda:G_K\rightarrow GL_n(\overline E_\lambda)\}$ be a semisimple E-rational compatible system of a number field K. In a first step, building upon the theory of pseudocharacters [Ro96],[Ch14], we attach to each $\rho_\lambda$…

Let $F$ be a totally real field and $n\leq 4$ a natural number. We study the monodromy groups of any $n$-dimensional strictly compatible system $\{\rho_\lambda\}_\lambda$ of $\lambda$-adic representations of $F$ with distinct Hodge-Tate…

Let $X$ be a smooth, separated, geometrically connected scheme defined over a number field $K$ and $\{\rho_\lambda\}_\lambda$ a system of n-dimensional semisimple $\lambda$-adic representations of the \'etale fundamental group of $X$ such…

Let $K$ be a totally real field and $\pi$ be a regular algebraic polarized cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb A_K)$. Let $\{\rho_{\pi,\lambda}:\mathrm{Gal}_K\to\mathrm{GL}_n(\overline E_\lambda)\}_\lambda$ be the…

Let $X$ be a generic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p\geq 0$. We show that for $n$ sufficiently large there exists a tame rational map $f:X\to \PP^1_k$ with monodromy group $A_n$. This…

Let X be a smooth curve over a finite field of characteristic p, let E be a number field, and consider an E-compatible system of lisse sheaves on the curve X. For each place lambda of E not lying over p, the lambda-component of the system…

Let $F$ be an algebraically closed field of characteristic $p$. We fashion an infinite dimensional basic algebra $\underleftarrow{\mathcal{C}}_p(F)$, with a transparent combinatorial structure, which we expect to control the rational…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our…

In this article we introduce the notion of a quasi-compatible system of Galois representations. The quasi-compatibility condition is a slight relaxation of the classical compatibility condition in the sense of Serre. The main theorem that…

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonn\'e modules of abelian varieties defined over global function fields of characteristic $p$. As a corollary we…

Let $k$ be an uncountable algebraically closed field of characteristic $0$, and let $X$ be a smooth projective connected variety of dimension $2p$, appropriately embedded into $\mathbb P^m$ over $k$. Let $Y$ be a hyperplane section of $X$,…

Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…

Here we show that, given a finite homological system $({\cal P},\leq,\{\Delta_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules…

In this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…