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Equivariant vector bundles on the Lubin-Tate moduli space. (English) Zbl 0807.14037

Friedlander, Eric M. (ed.) et al., Topology and representation theory. Conference on the connections between topology and representation theory held at Northwestern University, Evanston, IL (USA), May 1-5, 1992. Providence, RI: American Mathematical Society. Contemp. Math. 158, 23-88 (1994).
Let \(A\) be a complete discrete valuation ring with finite residue field, and let \(F\) be a formal \(A\)-module of dimension 1 and height \(n\). The authors study the moduli space of deformations of \(F\), \(X = \text{Spf} A[[u_ 1, \dots, u_{n - 1}]]\), endowed with the natural action of the étale group scheme \(G = \operatorname{Aut} (F)\). They make use of the theory of universal additive extensions \(E\) of \(F\) to construct some natural \(G\)- equivariant vector bundles on \(X\). From these vector bundles they are able to recover the tangent bundle of \(X\), the bundle of exterior \(i\)- forms, and the canonical bundle of \(X\). In the case when \(A\) is the ring of \(p\)-adic integers, some of the result proved in the paper under review, had been obtained before by Lubin and Tate.
The paper is written in a selfcontained way, in particular including (and extending) some known results due to several people such as: Lubin, Tate, Lazard, Honda, Cartier, Drinfeld, Hazewinkel, and others.
For the entire collection see [Zbl 0785.00029].

MSC:

14L05 Formal groups, \(p\)-divisible groups
12H25 \(p\)-adic differential equations
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14L30 Group actions on varieties or schemes (quotients)
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