Topic
Néron model
About: Néron model is a research topic. Over the lifetime, 59 publications have been published within this topic receiving 652 citations. The topic is also known as: Neron model.
Papers published on a yearly basis
Papers
1 Jan 1977
TL;DR: Ueno and Shioda as discussed by the authors gave a classification of Hilbert modular surfaces with pencils of curves genus 2 E. van der Geer and A. van de Ven Part II: 10. Relative compactification of the Neron model and its application I.
Abstract: Foreword List of contributors Introduction K. Ueno and T. Shioda Part I: 1. Coverings of the rational double points in characteristic p M. Artin 2. Entriques' classification of surfaces in char p, II E. Bombieri and D. Mumford 3. Classification of Hilbert modular surfaces F. Hirzebruch and D. Zagier 4. On algebraic surfaces with pencils of curves genus 2 E. Horikawa 5. New surfaces with no meromorphic functions, II M. Inoue 6. On the deformation types of regular elliptic surfaces A. Kas 7. On numerical Campedelli surfaces Y. Miyaoka 8. On singular K3 surfaces T. Shioda and H. Inose 9. On the minimality of certain Hilbert modular surfaces G. van der Geer and A. Van de Ven Part II: 10. Complex structures on S2p + 1 X S2q + 1 with algebraic codimension 1 K. Akao 11. Defining equations for certain types of polarized varieties T. Fujita 12. On logarithmic Kodaira dimension of algebraic varieties S. Iitaka 13. On a characterization of submanifolds of Hopf manifolds Ma. Kato 14. Relative compactification of the Neron model and its application I. Nakamura 15. Toroidal degeneration of Abelian varieties Y. Namikawa 16. Kodaira dimensions of complements of divisors F. Sakai 17. Compact quotients of C3 by affine transformation groups, II T. Suwa 18. Kodaira dimensions for certain fibre spaces K. Ueno Part III: 19. Some remarks on formal Poincare lemma A. Andreotti and M. Nacinovich 20. Special arithmetic groups and Eisenstein series W. L. Baily, Jr. 21. Submanifolds and over-determined differential operators H. Goldschmidt and D. Spencer 22. On the first terms of certain asymptotic expansions J. Igusa 23. Micro-local calculus of simple microfunctions M. Kashiwara 24. A note on Steenrod reduced powers of algebraic cocycles S. Kawai 25. Polynomicl growth C -de Rahm cosmology and normalized series of prestratified spaces N. Sasakura Index.
109 citations
TL;DR: In this paper, the authors construct modular Deligne-Mumford stacks representable over parametrizing Neron models of Jacobians as follows: if B is a smooth curve and K its function field, let be a smooth genus-g curve over K admitting stable minimal model over B. The Neron model is then the base change of via the moduli map B? of f, i.e., B.
Abstract: We construct modular Deligne-Mumford stacks representable over parametrizing Neron models of Jacobians as follows. Let B be a smooth curve and K its function field, let be a smooth genus-g curve over K admitting stable minimal model over B. The Neron model ? B is then the base change of via the moduli map B ? of f , i.e.: B. Moreover is compactified by a Deligne-Mumford stack over , giving a completion of Neron models naturally stratified in terms of Neron models.
63 citations
TL;DR: Neron models as discussed by the authors are a smooth group scheme of finite type over O, characterized by the property that for every finite unramified extension L of K, every L-valued point of AK extends uniquely to an OL-valued points of A. In general, the formation of Neron models does not commute with base change.
Abstract: 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 Neron model A over O. The Neron model A of A is a smooth group scheme of finite type over O, characterized by the property that for every finite unramified extension L of K, every L-valued point of AK extends uniquely to an OL-valued point of A. We refer to the book [BLR] for a thorough exposition of the construction and basic properties of Neron models. In general, the formation of Neron models does not commute with base change. Rather, for every finite extension field M of K, we have a canonical homomorphism
54 citations
TL;DR: In this paper, it was shown that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes, the Galois group of the splitting field of the ''-torsion of A is GSp2g(Z/`).
Abstract: Let K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes `, the Galois group of the splitting field of the `-torsion of A is GSp2g(Z/`).
51 citations
TL;DR: In this article, the authors studied the set of rational points of the group of components of an abelian variety over a discrete valuation field K. In particular, they looked at the cases where A_K is a Jacobian or a semiautomain variety having semi-stable reduction.
Abstract: Let A_K be an abelian variety over a discrete valuation field K. Let A be the Neron model of A_K over the ring of integers O_K of K and A_k its special fibre. We study the set of rational points of the group of components \phi_A of A_k. In particular, we look at the cases where A_K is a Jacobian or where A_K is an abelian variety having semi-stable reduction. We also consider algebraic tori over K instead of abelian varieties.
49 citations
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| 2017 | 1 |