Eknath Ghate

activity

20112026

most citedReduction of Galois Representations of slope 1

21 citations · 61 across the 24 of their papers we have counts for

collaborators

26 papers

math.NT2026

Reductions of Galois representations of slope $2$

Eknath Ghate, Sudipta Majumder

Let $p$ be a prime $\geq 5$ . We determine the semisimplifications of the mod $p$ reductions of irreducible two-dimensional crystalline representations of the Galois group of ${\math…

math.NT2026

Which numbers are $u$ -invariants of perfectoid fields?

Eknath Ghate, Srinivasan Srimathy

Let $p \neq = 2$ be a prime. We determine the set of numbers that occur as the $u$ -invariant of perfectoid subfields of $C_{p}$ . Given any number that is the $u$ -invariant of a…

math.NT2026

Reductions Of Crystalline Representations Of Fractional Slope $< p - 1$

Shalini Bhattacharya, Eknath Ghate, Ravitheja Vangala

Let $p$ be an odd prime and let $V_{k, a_{p}}$ be the two-dimensional crystalline representation of the Galois group of $Q_{p}$ of weight $k \geq 2$ and parameter $a_p \in \ba…

math.NT2026

Reductions of $GL_{2} (Q_{p^{f}})$ -Banach spaces of slopes in $(0, 1)$

Eknath Ghate, Shivansh Pandey

Let $p$ be an odd prime and $f \geq 1$ . We consider a $p$ -adic locally algebraic $GL_{2} (Q_{p^{f}})$ -representation attached to a tuple of $f$ weights $k = (k_{i})$ for $0 \…

math.NT2026

Reduction mod $p$ of semi-stable representations of some super-Breuil weights

Anand Chitrao, Eknath Ghate

We determine the mod $p$ reductions of the semi-stable representations $V_{k, L}$ of weight $k \in [p + 5, 2 p] \cup [2 p + 6, 3 p + 1]$ and $v_{p} (L) < 1 - k /2$ for pri…

math.NT2026★ 15 cited

On the Brauer class of Modular Endomorphism Algebras

Enrique González-Jiménez, Eknath Ghate, Jordi Quer

We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the…

math.NT2025

The semi-stable Local Langlands Correspondence

Eknath Ghate

We start with background that goes into an Iwahori-theoretic reformulation of the mod $p$ Local Langlands Correspondence (§2). We then explain some classical $p$ -adic functional an…

math.RT2025

Clebsch-Gordan and the theta filtration for modular representations of $GL_{2} (F_{q})$

Srijeet Bhattacharjee, Eknath Ghate, Shivansh Pandey +1

Let $p$ be a prime. We solve two problems in the mod $p$ representation theory of $GL_{2} (F_{q})$ where $q = p^{f}$ . We first prove a Clebsch-Gordan decomposition theor…

math.RT2025

Restriction problem for mod $p$ representations of $GL_{2}$ over a finite field

Eknath Ghate, Shubhanshi Gupta

Let $F_{q}$ be the finite field with $q = p^{f}$ elements. We study the restriction of two classes of mod $p$ representations of $G_{q} = GL_{2} (F_{q})$ to $G_p =…

math.NT2025

Deformations of reducible Galois representations with large Selmer $p$ -rank

Eknath Ghate, Anwesh Ray

Let $p \geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$ -torsion in the Bloch-Kato Selme…

math.NT2023★ 1 cited

Reductions of semi-stable representations using the Iwahori mod $p$ Local Langlands Correspondence

Anand Chitrao, Eknath Ghate

We determine the mod $p$ reductions of all two-dimensional semi-stable representations $V_{k, L}$ of the Galois group of $Q_{p}$ of weights $3 \leq k \leq p + 1$ and…

math.RT2023★ 1 cited

Modular representations of $GL_{2} (F_{q})$ using calculus

Eknath Ghate, Arindam Jana

We show that certain modular induced representations of $GL_{2} (F_{q})$ can be written as cokernels of operators acting on symmetric power representations of $\mathr…

math.NT2022★ 1 cited

Zig-zag for Galois Representations

Eknath Ghate

The zig-zag conjecture says that the reductions of two-dimensional crystalline representations of the Galois group of $Q_{p}$ of large exceptional weights and half-integr…

math.RT2022★ 2 cited

Non-admissible irreducible representations of $p$ -adic $GL_{n}$ in characteristic $p$

Eknath Ghate, Daniel Le, Mihir Sheth

Let $p > 3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $F_{p}$ . We construct smooth absolutely irreducible non-admissible represe…

math.NT2021★ 3 cited

Semi-stable representations as limits of crystalline representations

Anand Chitrao, Eknath Ghate, Seidai Yasuda

We construct an explicit sequence $V_{k_{n}, a_{n}}$ of crystalline representations of exceptional weights converging to a given irreducible two-dimensional semi-stable representation $…

math.RT2020

On non-admissible irreducible modulo $p$ representations of $G L_{2} (Q_{p^{2}})$

Eknath Ghate, Mihir Sheth

We use a Diamond diagram attached to a $2$ -dimensional reducible split mod $p$ Galois representation of $Gal (Q_{p} / Q_{p^{2}})$ to construct a…

math.NT2019★ 3 cited

$p$ -adic Asai $L$ -functions attached to Bianchi cusp forms

Baskar Balasubramanyam, Eknath Ghate, Ravitheja Vangala

We establish a rationality result for the twisted Asai L-values attached to a Bianchi cusp form and construct distributions interpolating these L-values. Using the method of abstra…

math.NT2019

Reductions of Galois representations and the theta operator

Eknath Ghate, Arvind Kumar

Let $p \geq 5$ be a prime, and let $f$ be a cuspidal eigenform of weight at least $2$ and level coprime to $p$ of finite slope $α$ . Let $ρ ˉ_{f}$ denote the mod $p$ Galois representa…

math.RT2019

The Monomial Lattice in Modular Symmetric Power Representations

Eknath Ghate, Ravitheja Vangala

Let $p$ be a prime. We study the structure of and the inclusion relations among the terms in the monomial lattice in the modular symmetric power representations of $\mathrm{GL}_2(\…

math.NT2019★ 7 cited

A zig-zag conjecture and local constancy for Galois representations

Eknath Ghate

We make a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{Q_{p}}$ of half-integral slopes and exceptional weig…

math.NT2019

$p$ -adic Rankin product $L$ -functions

Eknath Ghate, Ravitheja Vangala

We describe Panchishkin's construction of the $p$ -adic Rankin product $L$ -function.

math.NT2019★ 3 cited

Reductions of Galois representations of Slope $\frac{3}{2}$

Eknath Ghate, Vivek Rai

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{Q_{p}}$ of slope $\frac{3}{2}$ and exceptional weig…

math.NT2016

Sums of Fractions and Finiteness of Monodromy

Eknath Ghate, T. N. Venkataramana

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy represe…

math.NT2015★ 21 cited

Reduction of Galois Representations of slope 1

Shalini Bhattacharya, Eknath Ghate, Sandra Rozensztajn

We compute the reductions of irreducible crystalline two-dimensional representations of $G_{Q_{p}}$ of slope 1, for primes $p \geq 5$ , and all weights. We describe the semis…

Reductions of Galois representations of slope 2

Which numbers are u-invariants of perfectoid fields?

Reductions Of Crystalline Representations Of Fractional Slope <p−1

Reductions of GL2​(Qpf​)-Banach spaces of slopes in (0,1)

Reduction mod p of semi-stable representations of some super-Breuil weights

On the Brauer class of Modular Endomorphism Algebras

The semi-stable Local Langlands Correspondence

Clebsch-Gordan and the theta filtration for modular representations of GL2​(Fq​)

Restriction problem for mod p representations of GL2​ over a finite field

Deformations of reducible Galois representations with large Selmer p-rank

Reductions of semi-stable representations using the Iwahori mod p Local Langlands Correspondence

Modular representations of GL2​(Fq​) using calculus

Zig-zag for Galois Representations

Non-admissible irreducible representations of p-adic GLn​ in characteristic p

Semi-stable representations as limits of crystalline representations

On non-admissible irreducible modulo p representations of GL2​(Qp2​)

p-adic Asai L-functions attached to Bianchi cusp forms

Reductions of Galois representations and the theta operator

The Monomial Lattice in Modular Symmetric Power Representations

A zig-zag conjecture and local constancy for Galois representations

p-adic Rankin product L-functions

Reductions of Galois representations of Slope 23​

Sums of Fractions and Finiteness of Monodromy

Reduction of Galois Representations of slope 1

Reductions of Galois representations of slope $2$

Which numbers are $u$ -invariants of perfectoid fields?

Reductions Of Crystalline Representations Of Fractional Slope $< p - 1$

Reductions of $GL_{2} (Q_{p^{f}})$ -Banach spaces of slopes in $(0, 1)$

Reduction mod $p$ of semi-stable representations of some super-Breuil weights

Clebsch-Gordan and the theta filtration for modular representations of $GL_{2} (F_{q})$

Restriction problem for mod $p$ representations of $GL_{2}$ over a finite field

Deformations of reducible Galois representations with large Selmer $p$ -rank

Reductions of semi-stable representations using the Iwahori mod $p$ Local Langlands Correspondence

Modular representations of $GL_{2} (F_{q})$ using calculus

Non-admissible irreducible representations of $p$ -adic $GL_{n}$ in characteristic $p$

On non-admissible irreducible modulo $p$ representations of $G L_{2} (Q_{p^{2}})$

$p$ -adic Asai $L$ -functions attached to Bianchi cusp forms

$p$ -adic Rankin product $L$ -functions

Reductions of Galois representations of Slope $\frac{3}{2}$