arXiv subjects

Alireza Shavali

Publications and source records attributed to Alireza Shavali.

4 recordsLinked to original sources

arXiv2026

Irreducibility and Monodromy of Automorphic Galois Representations of $\mathrm{GL}(4)$

We prove that over totally real fields, the $p$-adic Galois representations attached to non-self-dual regular algebraic cuspidal automorphic representations of $\mathrm{GL}(4)$ are irreducible. We then develop the theory of extra-twists in a general setting and use it to compute the monodromy group (over $\mathbb{Q}$) of these Galois representations, in both self-dual and non-self-dual settings, and prove $p$-adic and residual big image results.

math.NT↗

arXiv2025

On The Image of Automorphic Galois Representations

In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic representations of $\mathrm{GL}_3$ over totally real fields. We also formulate a conjecture for the $\mathrm{GL}_n$-case and show how it follows from some standard conjectures in the Langlands program. Finally, assuming the existence of a motive associated with the representation, we study the relation of our constructions with the Mumford-Tate group.

math.NT↗

arXiv2024

On the Endomorphism Algebra of Abelian Varieties Associated with Hilbert Modular Forms

In this article, we will generalize an explicit formula proved by Quer for the Brauer class of the endomorphism algebra of abelian varieties associated to modular forms of weight 2 to the case of Hilbert modular forms of parallel weight 2, under the condition that the degree of the base field over Q is an odd number.

math.NT↗

arXiv2021

New Bounds on the Biplanar and $k$-Planar Crossing Numbers

The biplanar crossing number of a graph $G$ is the minimum number of crossings over all possible drawings of the edges of $G$ in two disjoint planes. We present new bounds on the biplanar crossing number of complete graphs and complete bipartite graphs. In particular, we prove that the biplanar crossing number of complete bipartite graphs can be approximated to within a factor of $3$, improving over the best previously known approximation factor of $4.03$. For complete graphs, we provide a new approximation factor of $3.17$, improving over the best previous factor of $4.34$. We provide similar improved approximation factors for the $k$-planar crossing number of complete graphs and complete bipartite graphs, for any positive integer $k$. We also investigate the relation between (ordinary) crossing number and biplanar crossing number of general graphs in more depth, and prove that any graph with a crossing number of at most $10$ is biplanar.

cs.CG↗