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Hi All,

Where can I find a proof of the Hodge-Tate decomposition for Lubin-Tate formal groups?


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This is essentially done in Serre's article in Cassels-Frohlich (see also his book 'abelian l-adic representations and elliptic curves', appendix to chapter 3). – user1594 Dec 2 '10 at 18:25
There's an appendix in Serre's book "Abelian $\ell$-adic representations" which discusses special features of the abelian semisimple case (including Lubin-Tate groups as a special case), so you may also find that to be instructive. – BCnrd Dec 3 '10 at 4:53
up vote 6 down vote accepted

Dear jjj,

I recommend reading Tate's original paper, which proves the Hodge--Tate decomposition for all $p$-divisible groups. If you are nervous about $p$-divisible groups, rather than formal groups, it would not be difficult to restrict to just this case while reading the paper. (And the paper includes an entire section devoted to relating formal groups to the $p$-divisible groups picture, which is valuable in its own right.)

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I don't know if jjj knows where to find Tate's original article so I may add that it is in : Proceedings of a Conference on Local Fields, Springer, 1967. – A M Dec 2 '10 at 19:45

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