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Serre–Tate theorem

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This is an old revision of this page, as edited by 89.3.143.85 (talk) at 16:12, 28 December 2016 (The reference to Serre-Tate's paper was irrelevant; I have given instead a reference to my correspondence with Tate, published in 2015 by the Societe Mathematique de France. JPS). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In algebraic geometry, the Serre–Tate theorem, Serre and Tate (1964) says that an abelian scheme and its p-divisible group have the same infinitesimal deformation theory. This was first proved by Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then Tate gave a proof in the general case by a different method. Their proofs were not published, but they were summarized in the notes of the Lubin-Serre-Tate seminar (Woods Hole, 1964). Other proofs were published by Messing (1962) and Drinfeld (1976).

References

  • Colmez, Pierre; Serre, Jean-Pierre, Correspondance Serre-Tate, SMF 2015 : see, vol.2, p.854, comments on Tate's letter from Jan.10, 1964.


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