数论讨论班

3月13日 (周五)

16:00–17:00

光华楼东主楼 2001

吴志翔

(中国科学技术大学)

Title: Breuil-Strauch conjecture for the Lubin-Tate space of dimension $1$.

Abstract: In the $p$-adic local Langlands program, the Breuil-Strauch conjecture predicts that certain representations of $\mathrm{GL}_2(\mathbb{Q}_p)$, arising from equivariant vector bundles on the one-dimensional Drinfeld space, are closely related to two-dimensional $p$-adic de Rham Galois representations. This conjecture was proved by Dospinescu-Le Bras. In this talk, we present an analogous picture for the one-dimensional Lubin-Tate space. In this setting, the cohomology of equivariant vector bundles naturally produces representations of the unit group of the non-split quaternion algebra over $\mathbb{Q}_p$, which may be viewed as the Jacquet-Langlands counterpart of $\mathrm{GL}_2(\mathbb{Q}_p)$. Using global methods introduced by Lue Pan, we explain how these representations relate to $p$-adic Galois representations and clarify certain features of the $p$-adic Jacquet-Langlands correspondence. This is joint work with Benchao Su and Zhenghui Li.

4月10日 (周五)

16:00–17:00

SCMS

Title.

Abstract.