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| Rational Structure of X(N) over Qand Explicit Galois Action on CM Points |
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Citation： |
Tonghai YANG.Rational Structure of X(N) over Qand Explicit Galois Action on CM Points[J].Chinese Annals of Mathematics B,2016,37(6):821~832 |
| Page view： 1778
Net amount： 1323 |
Authors： |
Tonghai YANG; |
Foundation： |
This work was supported by the National Science
Foundation Grants (No.DMS-1200380, DMS-1500743) and the Chinese
Qian Ren Plan of Tsinghua (No.543100001). |
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| Abstract： |
This paper reviews a less known rational structure on the Siegel
modular variety $X(N) =\Gamma(N) \backslash \H_g$ over $\Q$ for
integers $g, N \ge 1$. The author then describes explicitly how
Galois groups act on CM points on this variety. Finally, another
proof of the Shimura reciprocity law by using the result and the
$q$-expansion principle is given. |
Keywords： |
modular variety, Galois action, Explicit reciprocity law |
Classification： |
11G18, 14G40, 11F67 |
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