scholarly journals Groups of components of Néron models of Jacobians and Brauer groups

2015 ◽  
Vol 11 (02) ◽  
pp. 621-629 ◽  
Author(s):  
Saikat Biswas
Keyword(s):  
Local Field ◽  
Brauer Group ◽  
Brauer Groups ◽  
Component Group ◽  
Neron Models ◽  
Néron Models

Let X be a proper, smooth, and geometrically connected curve over a non-archimedean local field K. In this paper, we relate the component group of the Néron model of the Jacobian of X to the Brauer group of X.

scholarly journals Optimal Quotients of Jacobians With Toric Reduction and Component Groups

2016 ◽  
Vol 68 (6) ◽  
pp. 1362-1381
Author(s):  
Mihran Papikian ◽  
Joseph Rabinoff
Keyword(s):  
Elliptic Curve ◽  
Local Field ◽  
Modular Curves ◽  
Jacobian Variety ◽  
Neron Models ◽  
Néron Models

AbstractLet J be a Jacobian variety with toric reduction over a local field K. Let J → E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the functorially induced map on component groups of the Néron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which is surjective and discuss when these criteria hold for the Jacobians of modular curves.

scholarly journals Crystalline subrepresentations and Neron models

2000 ◽  
Vol 7 (5) ◽  
pp. 605-614
Author(s):  
Minhyong Kim ◽  
Susan H. Marshall
Keyword(s):  
Neron Models ◽  
Néron Models

Néron models

2017 ◽  
Vol 3 (2) ◽  
pp. 171-198
Author(s):  
Dino Lorenzini
Keyword(s):  
Neron Models ◽  
Néron Models

scholarly journals Néron models and limits of Abel–Jacobi mappings

2010 ◽  
Vol 146 (2) ◽  
pp. 288-366 ◽  
Author(s):  
Mark Green ◽  
Phillip Griffiths ◽  
Matt Kerr
Keyword(s):  
Normal Function ◽  
Motivic Cohomology ◽  
Normal Functions ◽  
Geometric Setting ◽  
Neron Models ◽  
A Finite Group ◽  
Intermediate Jacobian ◽  
Néron Models ◽  
Singular Fibre ◽  
Finite Singularity

AbstractWe show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on motivic cohomology of the singular fibre, hence via regulators onK-groups of its substrata. Two examples are worked out in detail, for families of 1-cycles on CY and abelian 3-folds, where this produces interesting arithmetic constraints on such limits. We also show how to compute the finite ‘singularity group’ in the geometric setting.

A Note on the Height of the Formal Brauer Group of a K3 Surface

2004 ◽  
Vol 47 (1) ◽  
pp. 22-29 ◽  
Author(s):  
Yasuhiro Goto
Keyword(s):  
Positive Characteristic ◽  
Brauer Group ◽  
K3 Surface ◽  
Brauer Groups

AbstractUsing weighted Delsarte surfaces, we give examples of K3 surfaces in positive characteristic whose formal Brauer groups have height equal to 5, 8 or 9. These are among the four values of the height left open in the article of Yui [11].

Néron Models

1986 ◽  
pp. 213-230 ◽  
Author(s):  
M. Artin
Keyword(s):  
Neron Models ◽  
Néron Models

Néron models, Lie algebras, and reduction of curves of genus one

2004 ◽  
Vol 157 (3) ◽  
pp. 455-518 ◽  
Author(s):  
Qing Liu ◽  
Dino Lorenzini ◽  
Michel Raynaud
Keyword(s):  
Lie Algebras ◽  
Neron Models ◽  
Genus One ◽  
Néron Models ◽  
Reduction Of Curves
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