Models of Z/p^2 Z over a d.v.r. of unequal characteristic

Details Models of Z/p^2 Z over a d.v.r. of unequal characteristic Models of Z/p^2 Z over a d.v.r. of unequal characteristic

2008-03-26

arxiv.org/abs/0803.3702v1

Mathematics

Algebraic Geometry

40 pages

Scientific paper

Let R be a discrete valuation ring of unequal characteristic which contains a primitive p^2-th root of unity. If K is the fraction field of R, it is well known that (Z/p^2 Z)_K is isomorphic to \mu_{p^2,K}. We prove that any finite and flat R-group scheme of order p^2 isomorphic to (Z/p^2 Z)_K on the generic fiber (i.e. a model of (Z/p^2 Z)_K), is the kernel in a short exact sequence which generically coincides with the Kummer sequence. We will explicitly describe and classify such models.

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