Abstract: We discuss recent developments in the Langlands program for function fields. In particular we explain a canonical decomposition of the space of cuspidal automorphic forms for any reductive group G over a function field, indexed by global Langlands parameters. The proof uses the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence.
https://eta.impa.br/dl/PL022.pdf
https://arxiv.org/abs/1803.03791
本文讨论函数域上的Langlands对应。作者给出函数域上任意约化群的尖性自守形式空间的典范直和分解，其直和项取遍整体Langlands参数。为此，作者推广了Drinfeld以及L. Lafforgue的штука的模空间的方法，并运用了几何Langlands纲领中的几何Satake等价性。但是，数域上相应的结果仍然未知。
相关附件
21-PL022 Lafforgue
