J. Shotton

activity

20132026

most citedThe Breuil--Mézard conjecture when

l \neq = p

19 citations · 53 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2026

The Smallest Invariant Factor of Elliptic Curves, and Coincidences

Alexander Milner, Jack Shotton

For an elliptic curve E over Q and a natural number j, Cojocaru has shown that there is an explicit constant C_E,j giving (under GRH) the density of primes p of good reduction such…

math.NT2024

Singularities of Steinberg deformation rings

Daniel Funck, Jack Shotton

Let $l$ and $p$ be distinct primes, let $F$ be a local field with residue field of characteristic $p$ , and let $X$ be the irreducible component of the moduli space of La…

math.NT2023★ 1 cited

Irreducible components of the moduli space of Langlands parameters

Jack Shotton

Let $F / Q_{p}$ be finite and let $X_{G}$ be the moduli space of Langlands parameters valued in $G$ , in characteristic distinct from $p$ . First, we determine the irre…

math.RT2022★ 3 cited

On endomorphism algebras of Gelfand-Graev representations II

Tzu-Jan Li, Jack Shotton

Let $G$ be a connected reductive group defined over a finite field $F_{q}$ of characteristic $p$ , with Deligne--Lusztig dual $G^{*}$ . We show that, over $\overline{\mathbb{…

math.NT2020★ 2 cited

Generic local deformation rings when $l \neq = p$

Jack Shotton

We determine the local deformation rings of sufficiently generic mod $l$ representations of the Galois group of a $p$ -adic field, when $l \neq = p$ , relating them to the space of $q$ …

math.NT2019★ 11 cited

Ihara's lemma for Shimura curves over totally real fields via patching

Jeff Manning, Jack Shotton

We prove Ihara's lemma for the mod $l$ cohomology of Shimura curves, localised at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois repr…

math.RT2017★ 1 cited

On the category of finitely presented mod $p$ representations of $G L_{2} (F)$

Jack Shotton

Let $F$ be a finite extension of $Q_{p}$ . We prove that the category of finitely presented smooth $Z$ -finite representations of $G L_{2} (F)$ over a finite extension of $\mathbb…

math.NT2016★ 19 cited

The Breuil--Mézard conjecture when $l \neq = p$

Jack Shotton

Let $l$ and $p$ be primes, let $F / Q_{p}$ be a finite extension with absolute Galois group $G_{F}$ , let $F$ be a finite field of characteristic $l$ , and let $\barρ : G…

math.NT2013★ 16 cited

Local deformation rings and a Breuil-Mézard conjecture when l\neq p

Jack Shotton

We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite…

The Smallest Invariant Factor of Elliptic Curves, and Coincidences

Singularities of Steinberg deformation rings

Irreducible components of the moduli space of Langlands parameters

On endomorphism algebras of Gelfand-Graev representations II

Generic local deformation rings when l=p

Ihara's lemma for Shimura curves over totally real fields via patching

On the category of finitely presented mod p representations of GL2​(F)

The Breuil--Mézard conjecture when l=p

Local deformation rings and a Breuil-Mézard conjecture when l\neq p

Generic local deformation rings when $l \neq = p$

On the category of finitely presented mod $p$ representations of $G L_{2} (F)$

The Breuil--Mézard conjecture when $l \neq = p$