Eknath Ghate

activity

20242026

collaborators

12 papers

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

On the Brauer class of Modular Endomorphism Algebras

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 (Â§2). We then explain some classical $p$ -adic functional a…

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

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