记些杂七杂八的感想.
本系列完全不定时更新.
From now on, we let be a surface.
Firstly, we aimed to calculate . Here we identify be the space of holomorphic line bundles on . Then we have a short exact sequence:
the degree line bundles. By the theory of Riemann Surface, one can topologically identify:
One can identify . Then we have abelian category equivalence
Secondly, we shall consider the algebraic geometry of the character scheme . To begin with, we can write the character scheme by
Then, by the theory of algebraic geometry, there are
With denote the global functions on . And we can identify as .
But by Fourier transform, we can identify
Hence we finally attains
从 Ben-Zvi 的一篇课程笔记: Between electric-magnetic duality and the Langlands program 抄过来的.
这个实际上是最最简单的 Betti Langlands Correspondence: 的 case.
水点轻松的先.
但是这也不轻松, 原文有一些 typo. Check 一下还有些麻烦的.