Daniel Barrera Salazar

activity

20172026

most citedFamilies of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

16 citations · 35 across the 11 of their papers we have counts for

collaborators

13 papers

math.NT2026

On periods of Elliptic curves

Daniel Barrera Salazar, Juan-Pablo Llerena-Córdova

Let $E$ be an elliptic curve over $Q$ having split multiplicative reduction at a prime number $p$ . We describe the tame part of the $L$ -invariant of $E$ at $p$ i…

math.NT2026

The non-abelian Leopoldt conjecture and equalities of $L$ -invariants

Daniel Barrera Salazar, Andrew Graham, Chris Williams

Let $G$ be a reductive group quasi-split at $p$ . Using arguments of Hansen--Thorne, we show that under the non-abelian Leopoldt conjecture (NALC), Hansen's $p$ -adic overconvergent…

math.NT2025

Local-global compatibility and the exceptional zero conjecture for GL(3)

Daniel Barrera Salazar, Andrew Graham, Chris Williams

We prove exceptional zero conjectures for $p$ -ordinary regular algebraic cuspidal automorphic representations of $GL_{3} (A)$ which are Steinberg at $p$ . We make no…

math.NT2025

Higher Hida theory for Drinfeld modular curves

Daniel Barrera Salazar, Héctor del Castillo, Giovanni Rosso

Inspired by the construction of Higher Hida theory of Boxer and Pilloni, we develop Higher Hida theory for the cohomology of the line bundles of Drinfeld modular forms on the Drinf…

math.NT2024

Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results

Daniel Barrera Salazar, Luis Santiago Palacios

Let $K$ be an imaginary quadratic field. In this article, we study the local geometry of the Bianchi eigenvariety around non-cuspidal classical points, in particular, ordinary non-…

math.NT2023

On the $2$ -Selmer group of Jacobians of hyperelliptic curves

Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría

Let $C$ be a hyperelliptic curve $y^{2} = p (x)$ defined over a number field $K$ with $p (x)$ integral of odd degree. The purpose of the present article is to prove lower and…

math.NT2022★ 2 cited

On the GL(2n) eigenvariety: branching laws, Shalika families and $p$ -adic $L$ -functions

Daniel Barrera Salazar, Mladen Dimitrov, Andrew Graham +2

In this paper, we prove that a $GL (2 n)$ -eigenvariety is étale over the (pure) weight space at non-critical Shalika points, and construct multi-variable $p$ -adic $L$ -functi…

math.NT2021

Overconvergent cohomology, $p$ -adic $L$ -functions and families for $GL (2)$ over CM fields

Daniel Barrera Salazar, Chris Williams

The use of overconvergent cohomology in constructing $p$ -adic $L$ -functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been estab…

math.NT2021

On $p$ -adic $L$ -functions for $G L_{2 n}$ in finite slope Shalika families

Daniel Barrera Salazar, Mladen Dimitrov, Chris Williams

In this paper, we propose and explore a new connection in the study of $p$ -adic $L$ -functions and eigenvarieties. We use it to prove results on the geometry of the cuspidal eigenva…

math.NT2020

On $2$ -Selmer groups and quadratic twists of elliptic curves

Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría

Let $K$ be a number field and $E / K$ be an elliptic curve with no $2$ -torsion points. In the present article we give lower and upper bounds for the $2$ -Selmer rank of $E$ in terms o…

math.NT2019★ 3 cited

Triple product p-adic L-functions for Shimura curves over totally real number fields

Daniel Barrera Salazar, Santiago Molina Blanco

Let F be a totally real number field. Using a recent geometric approach developed by Andreatta and Iovita we construct several variables p-adic families of finite slope quaternioni…

math.NT2018★ 16 cited

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

Daniel Barrera Salazar, Chris Williams, Carl Wang-Erickson

Let $K$ be an imaginary quadratic field. In this article, we study the eigenvariety for $GL_{2} / K$ , proving an étaleness result for the weight map at non-critical classical…

math.NT2017★ 14 cited

$L$ -invariants and exceptional zeros of Bianchi modular forms

Daniel Barrera Salazar, Chris Williams

Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F. In this paper, we prove an exceptional zero conjecture in the case wher…

On periods of Elliptic curves

The non-abelian Leopoldt conjecture and equalities of L-invariants

Local-global compatibility and the exceptional zero conjecture for GL(3)

Higher Hida theory for Drinfeld modular curves

Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results

On the 2-Selmer group of Jacobians of hyperelliptic curves

On the GL(2n) eigenvariety: branching laws, Shalika families and p-adic L-functions

Overconvergent cohomology, p-adic L-functions and families for GL(2) over CM fields

On p-adic L-functions for GL2n​ in finite slope Shalika families

On 2-Selmer groups and quadratic twists of elliptic curves