6 papers
On periods of Elliptic curves
Daniel Barrera Salazar, Juan-Pablo Llerena-Córdova
Let be an elliptic curve over having split multiplicative reduction at a prime number . We describe the tame part of the -invariant of at i…
The non-abelian Leopoldt conjecture and equalities of -invariants
Daniel Barrera Salazar, Andrew Graham, Chris Williams
Let be a reductive group quasi-split at . Using arguments of Hansen--Thorne, we show that under the non-abelian Leopoldt conjecture (NALC), Hansen's -adic overconvergent…
On -adic -functions for 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 -adic -functions and eigenvarieties. We use it to prove results on the geometry of the cuspidal eigenva…
Local-global compatibility and the exceptional zero conjecture for GL(3)
Daniel Barrera Salazar, Andrew Graham, Chris Williams
We prove exceptional zero conjectures for -ordinary regular algebraic cuspidal automorphic representations of which are Steinberg at . We make no…
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…
Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results
Daniel Barrera Salazar, Luis Santiago Palacios
Let 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-…