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Zbl 0866.14029
Yu, Jiu-Kang
On the moduli of quasi-canonical liftings. (English)
[J] Compos. Math. 96, No.3, 293-321 (1995). ISSN 0010-437X; ISSN 1570-5846/e

Let $K_0$ be a non-archimedean local field, $A_0$ its ring of integers, $\pi_0$ a prime element and $k_0$ the finite residue field. Denote by $K$ a finite separable extension of $K_0$, and let $A$, $\pi$, and $k$ be the corresponding constructs for $K$. The author describes the ring class field of any order ${\cal O}$ in $K$ by means of the Lubin-Tate moduli space that parametrizes liftings of formal $A_0$-modules with an endomorphism action by ${\cal O}$ (quasi-canonical liftings). Other properties of these liftings are studied; in particular the author computes the Newton polygon of the endomorphism induced by $\pi_0$, gives an explicit description of the Gross-Hopkins period map and then studies the valuational properties of the period map. Finally, he determines the endomorphisms of the canonical lifting (which means a lifting with the action of the maximal order in $K)$. These objects and their study were introduced by {\it B. Gross} [Invent. Math. 84, 321-326 (1986; Zbl 0597.14044)] in the case in which $K$ is a quadratic extension of $K_0$. The author generalizes all those results to an arbitrary separable extension.
[M.Candilera (Padova)]

MSC 2000:: *14L05 Formal groups
11S31 Class field theory for local fields
14G15 Finite ground fields

Keywords: separable extension of local ground field; formal modules; Lubin-Tate moduli space; Newton polygon; period map; canonical lifting

Citations: Zbl 0597.14044

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