Lecture 2 : Serre ’ s conjecture and more
نویسنده
چکیده
Remark. Apropos of reduction mod p: If V is a Qp-vector space and G ⊂ GL(V ) is a compact subgroup, then there exists a G-fixed lattice in V for the following reason. Pick any lattice L ⊂ V . Then the G-stabilizer of L is open and of finite index. So Λ = ∑ g∈G gL ⊂ V is also a lattice, and it is definitely G-stable. The same works with coefficients in any finite extension of Qp, or even in Qp (since we saw last time that in this latter case the image is contained in GLn(K) for some subfield K of finite degree over Qp.
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تاریخ انتشار 2010