M. Papikian

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20242026

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math.NT2026

Stabilization of isogeny spaces between supersingular Drinfeld modules

Giacomo Micheli, Mihran Papikian

Let $p$ be a prime of degree $d$ in $A = F_{q} [T]$ and let $I ¨ , I ¨ $ be supersingular Drinfeld modules of rank $r \geq 2$ in $A$ -characteristic $p$ . We…

math.NT2026

Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"

Valentijn Karemaker, Jeffrey Katen, Mihran Papikian

In this note we provide corrections to Theorem 5.4 of the paper ``Isomorphism classes of Drinfeld modules over finite fields'', arXiv:2209.15033. The main theorems of this paper, T…

math.NT2026

Rank metric codes from Drinfeld modules

Giacomo Micheli, Mihran Papikian

We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of…

math.NT2025

On ideal class groups of totally degenerate number rings

Ruben Hambardzumyan, Mihran Papikian

Let $I ¨ (x) \in Z [x]$ be a monic polynomial whose roots are distinct integers. We study the ideal class monoid and the ideal class group of the ring $Z [x] / (I ¨ (x))$ .…

math.NT2024

Ogg's conjectures over function fields

In the early 1970s, Andrew Ogg made several conjectures about the rational torsion points of elliptic curves over $Q$ and the Jacobians of modular curves. These conjecture…

math.NT2024

$D$ -elliptic sheaves and the Hasse principle

Keisuke Arai, Shin Hattori, Satoshi Kondo +1

Let $p$ be a rational prime, $q > 1$ a power of $p$ and $F = F_{q} (t)$ . For an integer $d \geq 2$ , let $D$ be a central division algebra over $F$ of dimension $d^{2}$ which is spli…

Stabilization of isogeny spaces between supersingular Drinfeld modules

Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"

Rank metric codes from Drinfeld modules

On ideal class groups of totally degenerate number rings

Ogg's conjectures over function fields

D-elliptic sheaves and the Hasse principle

$D$ -elliptic sheaves and the Hasse principle