arXiv subjects

Kegang Liu

Publications and source records attributed to Kegang Liu.

2 recordsLinked to original sources

arXiv2022

Local-global compatibility of mod $p$ Langlands program for certain Shimura varieties

We generalize the local-global compatibility result in arXiv:1506.04022 to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove a cuspidality criterion from type theory. We also deal with compatibility for torsion classes in the case of semisimple mod $p$ Galois representations with distinct irreducible components under certain flatness hypotheses.

math.NT↗

arXiv2021

A note on mod-$p$ local-global compatibility via Scholze's functor

We remove the semisimple condition in the mod-$p$ local-global compatibility result of arXiv:2106.10674. Namely, assuming flatness of $π_{\mathfrak{m}}^\vee$ and $\overlineσ_{\mathfrak{m}}|_{\mathrm{Gal}_{F^+_{\mathfrak{p}}}}$ being multiplicity free, we prove that $H^{n-1}_{\text{ét}}(\mathbb{P}_{\mathbb{C}_p}^{n-1}, \mathcal{F}_{π_{\mathfrak{m}}[\mathfrak{m}]})$ determines $\overlineσ_{\mathfrak{m}}|_{\mathrm{Gal}_{F^+_{\mathfrak{p}}}}$ uniquely. We give remarks on our assumptions at the end of this note.

math.NT↗