Algebra & Number Theory

Wild models of curves

Dino Lorenzini

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Let K be a complete discrete valuation field with ring of integers OK and algebraically closed residue field k of characteristic p>0. Let XK be a smooth proper geometrically connected curve of genus g>0 with X(K) if g=1. Assume that XK does not have good reduction and that it obtains good reduction over a Galois extension LK of degree p. Let YOL be the smooth model of XLL. Let H:= Gal(LK).

In this article, we provide information on the regular model of XK obtained by desingularizing the wild quotient singularities of the quotient YH. The most precise information on the resolution of these quotient singularities is obtained when the special fiber Ykk is ordinary. As a corollary, we are able to produce for each odd prime p an infinite class of wild quotient singularities having pairwise distinct resolution graphs. The information on the regular model of XK also allows us to gather insight into the p-part of the component group of the Néron model of the Jacobian of X.

Article information

Algebra Number Theory, Volume 8, Number 2 (2014), 331-367.

Received: 3 January 2013
Revised: 6 June 2013
Accepted: 16 July 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G20: Local ground fields
Secondary: 14G17: Positive characteristic ground fields 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx] 14J17: Singularities [See also 14B05, 14E15]

model of a curve ordinary curve cyclic quotient singularity wild ramification arithmetical tree resolution graph component group Néron model


Lorenzini, Dino. Wild models of curves. Algebra Number Theory 8 (2014), no. 2, 331--367. doi:10.2140/ant.2014.8.331.

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