Algebra & Number Theory
- Algebra Number Theory
- Volume 8, Number 2 (2014), 331-367.
Wild models of curves
Let be a complete discrete valuation field with ring of integers and algebraically closed residue field of characteristic . Let be a smooth proper geometrically connected curve of genus with if . Assume that does not have good reduction and that it obtains good reduction over a Galois extension of degree . Let be the smooth model of . Let .
In this article, we provide information on the regular model of obtained by desingularizing the wild quotient singularities of the quotient . The most precise information on the resolution of these quotient singularities is obtained when the special fiber is ordinary. As a corollary, we are able to produce for each odd prime an infinite class of wild quotient singularities having pairwise distinct resolution graphs. The information on the regular model of also allows us to gather insight into the -part of the component group of the Néron model of the Jacobian of .
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
Permanent link to this document
Digital Object Identifier
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]
Lorenzini, Dino. Wild models of curves. Algebra Number Theory 8 (2014), no. 2, 331--367. doi:10.2140/ant.2014.8.331. https://projecteuclid.org/euclid.ant/1513730153