Special fibers of Néron models and wild ramification
@article{Liu2001SpecialFO, title={Special fibers of N{\'e}ron models and wild ramification}, author={Qing Liu and Dino J. Lorenzini}, journal={Crelle's Journal}, year={2001}, volume={2001} }
This mistake in [B-X] was first noted by Chai in [1], Remark 4.8 (2). Chai then notes that he was informed by Bosch that the mistake does not affect any other subsequent results in [B-X]. Our aim in this note is to carefully go through the proof of Proposition 1.8 in [2] and detail what results of [B-X] we use, so that the careful reader will be convinced that the proof of Proposition 1.8 is complete, and is not affected by the mistake in [B-X]. The comments on our original proof are in italic.
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References
SHOWING 1-10 OF 17 REFERENCES
On the arithmetic of abelian varieties
- Mathematics
- 1972
In w 1 we consider the situation: L/K is a finite separable field extension, A is an abelian variety over L, and A, is the abelian variety over K obtained from A by restriction of scalars. We study…
Neron models for semiabelian varieties: Congruence and change of base field
- Mathematics
- 2000
Let O be a henselian discrete valuation ring with perfect residue field. Denote by K the fraction field of O = OK , and by p = pK the maximal ideal of O. Then every abelian variety A over K has a…
Intersection numbers of sections of elliptic surfaces
- Mathematics
- 1979
The theory of elliptic surfaces over C draws on ideas and techniques from arithmetic, geometry and analysis. Let f : X ~ S be a minimal elliptic fibration with non-constant j-invariant, which…
Algorithms for Modular Elliptic Curves
- Computer Science, Mathematics
- 1992
This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation and an extensive set of tables giving the results of the author's implementations of the algorithms.
Arithmetic Duality Theorems
- Mathematics
- 1987
Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic…
Lorenzini , Special fibers of Néron models and wild ramification
- J . reine angew . Math .
- 2001
Special fibers of Néron models and wild ramification
- J. reine angew. Math
- 2001
The p-part of the group of components of a Néron model
- J. of Alg. Geom
- 1996