arXiv subjects

Chenji Fu

Publications and source records attributed to Chenji Fu.

2 recordsLinked to original sources

arXiv2025

On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the category of quasi-coherent sheaves on the connected component of the stack of L-parameters over Z_l-bar containing a tame, regular semisimple, elliptic L-parameter over F_l-bar. On the other hand, we describe the block of Rep_{Z_l-bar}G(F) containing a depth-zero regular supercuspidal irreducible representation πover F_l-bar. For G=GL_n, we compute both sides explicitly and verify the categorical local Langlands conjecture for depth-zero supercuspidal blocks.

math.RT↗

arXiv2024

Stability of Elliptic Fargues-Scholze $L$-packets

Let $F$ be a non-archimedean local field. Let $\overline{F}$ be an algebraic closure of $F$. Let $G$ be a connected reductive group over $F$. Let $φ$ be an elliptic $L$-parameter. For every irreducible representation $π$ of $G(F)$ with Fargues--Scholze $L$-parameter $φ$, we prove that there exists a finite set of irreducible representations $\{π_i\}_{i \in I}$ containing $π$, such that $π_i$ has Fargues--Scholze $L$-parameter $φ$ for all $i \in I$ and a certain non-zero $\mathbb{Z}$-linear combination $Θ_{π_0}$ of the Harish-Chandra characters of $\{π_i\}_{i \in I}$ is stable under $G(\overline{F})$ conjugation, as a function on the elliptic regular semisimple elements of $G(F)$. Moreover, if $F$ has characteristic zero, $Θ_{π_0}$ is a non-zero stable distribution on $G(F)$.

math.RT↗