Néron Models

Bosch, Siegfried; Lütkebohmert, Werner; Raynaud, Michel

doi:10.1007/978-3-642-51438-8

Cited by 950 publications

(1,520 citation statements)

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“…We use the characterization of smooth andétale maps given by Proposition 6 of § 2.2 of [1]; namely that it suffices to show that for any affine scheme Z → R T /S (Y ) and all closed sub-schemes Z 0 of Z whose ideal sheaf is square zero, the canonical map…”

Section: Fact 24 If T → S Is a Scheme Over S And F : X → Y Is A Smomentioning

confidence: 99%

Jet and prolongation spaces

Moosa

Scanlon

2010

J. Inst. Math. Jussieu

105

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Section: Fact 24 If T → S Is a Scheme Over S And F : X → Y Is A Smomentioning

confidence: 99%

Jet and prolongation spaces

Moosa

Scanlon

2010

J. Inst. Math. Jussieu

105

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“…In all the cases we consider Néron Models exist, see [BLR90]. In case of algebraically primitive Teichmüller curves, i.e.…”

Section: Teichmüller Curvesmentioning

confidence: 99%

“…Lines correspond to components of the semistable fibre, intersection points are nodes and Z 1 , Z 2 are the intersection points of the section s i with the stable fibre. Section 9.6 in [BLR90], 000 000 000 000 000 000 000 000 111 111 111 111 111 111 111 111 00 00 00 00 00 00 11 11 11 11 11 11 000 000 000 000 000 111 111 111 111 111 00 00 00 00 00 00 11 11 11 11 11 11 0 0 0 0 0 0 1 1 1 1 1 1 000 000 000 000 000 000 000 000 111 111 111 111 111 111 111 111 00 00 00 00 00 11 11 11 11 11 000 000 000 000 111 111 111 111 00 00 00 00 00 11 11 11 11 11 0 0 0 0 0 1 1 1 1 1 000 000 000 000 000 000 000 000 111 111 111 111 111 111 111 111 00 00 00 00 00 11 11 11 11 11 000 000 000 000 111 111 111 111 00 00 00 00 00 …”

Section: Degenerationsunclassified

Finiteness results for Teichmüller curves

Möller¹

2008

Ann. inst. Fourier

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“…For a model G of G, there exists a canonical smoothening morphism φ : G → G [BLR,7.1,Theorem 5], which is characterized by the following properties:…”

Section: Smootheningmentioning

confidence: 99%

“…After n and i n have been defined, we let n+1 be the dilatation of i n (Z κ ) on n . The dilatation of Z κ on Z, which is nothing but Z itself, then admits a natural closed immersion into n+1 by [BLR,3.2, Proposition 2(c)], which we denote by i n+1 .…”

Section: Higher Dilatationsmentioning

confidence: 99%

On quasi-reductive group schemes

Prasad

2006

J. Algebraic Geom.

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This paper was motivated by a question of Vilonen, and the main results have been used by Mirković and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over Z ) \mathbb {Z}) of a reductive group. We define a quasi-reductive group over a discrete valuation ring R R to be an affine flat group scheme over R R such that (i) the fibers are of finite type and of the same dimension; (ii) the generic fiber is smooth and connected, and (iii) the identity component of the reduced special fiber is a reductive group. We show that such a group scheme is of finite type over R R , the generic fiber is a reductive group, the special fiber is connected, and the group scheme is smooth over R R in most cases, for example when the residue characteristic is not 2, or when the generic fiber and reduced special fiber are of the same type as reductive groups. We also obtain results about group schemes over a Dedekind scheme or a Noetherian scheme. We show that in residue characteristic 2 there are non-smooth quasi-reductive group schemes with generic fiber SO 2 n + 1 \operatorname {SO}_{2n+1} and they can be classified when R R is strictly Henselian.

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Néron Models

Cited by 950 publications

References 0 publications

Jet and prolongation spaces

Jet and prolongation spaces

Finiteness results for Teichmüller curves

On quasi-reductive group schemes

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