Canonical liftings of formal modules. (English) Zbl 0635.14019

Tatevossion, Leon H.

Number theory, Proc. Conf., Montreal/Can. 1985, CMS Conf. Proc. 7, 457-463 (1987).

[For the entire collection see Zbl 0611.00005.]
Let \(A\) be the ring of integers in a complete discrete valuation field \(K\) with finite residue field. Let \(\mathfrak O\) be the ring of integers in a finite algebraic extension \(L\) of \(K\). Let \(M\) be the maximal unramified extension of \(K\), \(W\) the ring of integers in \(M\), \(y\) the maximal ideal in \(W\). Let \(G_{\text{LT}}\) be the Lubin-Tate formal group over \(\mathfrak O\) with multiplications from \(\mathfrak O\) [J. Lubin and J. Tate, Ann. Math. (2) 81, 380–387 (1965; Zbl 0128.26501)] and let \(G_{\text{LT}/W}:=G_{\text{LT}}\times_{\mathfrak O}W\) be the corresponding formal group over \(W\), viewed as formal \(A\)-(not \(\mathfrak O\))-module. In the case of unramified \(K\) the author computes the endomorphism rings of reductions of \(G_{\text{LT}/W}\) modulo powers of \(yW\).

Reviewer: Yu. G. Zarhin (Moskva)

MSC:

14L05	Formal groups, \(p\)-divisible groups
11S31	Class field theory; \(p\)-adic formal groups

Keywords:

liftings; Lubin-Tate formal group

Citations:

Zbl 0611.00005; Zbl 0128.26501