N\'eron models of formally finite type

@article{Kappen2011NeronMO,
  title={N\'eron models of formally finite type},
  author={Christian Kappen},
  journal={arXiv: Algebraic Geometry},
  year={2011}
}
We introduce N\'eron models of formally finite type for uniformly rigid spaces, and we prove that they generalize the notion of formal N\'eron models for rigid-analytic groups as it was defined by Bosch and Schl\"oter. Using this compatibility result, we give examples of uniformly rigid groups whose N\'eron models are not of topologically finite type. 
A refinement of the Artin conductor and the base change conductor
For a local field K with positive residue characteristic p, we introduce, in the first part of this paper, a refinement bAr_K of the classical Artin distribution Ar_K. It takes values in cyclotomic
Néron models
Néron models were introduced by André Néron in his seminar at the IHÉS in 1961. This article gives a brief survey of past and recent results in this very useful theory.

References

SHOWING 1-10 OF 52 REFERENCES
Uniformly rigid spaces and N\'eron models of formally finite type
We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces
Uniformly rigid spaces
We define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in
A generalization of formal schemes and rigid analytic varieties
In this paper we construct a natural category ~r of locally and topologically ringed spaces which contains both the category of locally noetherian formal schemes and the category of rigid analytic
Étale Cohomology of Rigid Analytic Varieties and Adic Spaces
Summary of the results on the etale cohomology of rigid analytic varieties - Adic spaces - The etale site of a rigid analytic variety and an adic space - Comparison theorems - Base change theorems -
Duality and flat base change on formal schemes
We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special
A few theorems on completion of excellent rings
In [2], chap. IV, 2 me partie, (7.4.8), Grothendieck considered the following problem: is any m-adic completion of an excellent ring A also excellent? In [8] I proved that, if A is an algebra of
Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes
This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf
Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes
This a first step to develop a theory of smooth, etale and unramified morphisms between noetherian formal schemes. Our main tool is the complete module of differentials, that is a coherent sheaf
Desingularization of quasi-excellent schemes in characteristic zero
Grothendieck proved in EGA IV that if any integral scheme of finite type over a locally noetherian scheme X admits a desingularization, then X is quasi-excellent, and conjectured that the converse is
A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
We establish a trace formula for rigid varieties X over a complete discretely valued field, which relates the set of unramified points on X to the Galois action on its étale cohomology. Next, we show
...
1
2
3
4
5
...