Timeline for Lang's proof of the Shimura's exact sequence
Current License: CC BY-SA 4.0
2 events
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| Oct 10, 2019 at 23:38 | comment | added | reuns | By definition of $F_\mathbf{C}=\bigcup_N \mathbf{C}(X(N))$ since $L$ is finitely generated it is contained in some $\mathbf{C}(X(N))$ so that $\{ A\in SL_2(\hat{\mathbf{Z}}), A\equiv I \bmod N\} \subset Aut(F_\mathbf{C}/ L)$. Also $SL_2(\hat{\mathbf{Z}})$ is the set of sequences $(A_m)$ in $M_2(\mathbf{Z})$ that converge modulo $n$ to an element of $SL_2(\mathbf{Z}/n\mathbf{Z})$ for all $n$, the automorphism is $f\mapsto \lim_{m \to \infty} f\circ A_m$. | |
| Oct 10, 2019 at 22:23 | history | asked | Shimrod | CC BY-SA 4.0 |