On the standard conjecture for projective compactifications of Neron models of 3-dimensional Abelian varieties

2021 ◽  
Vol 85 (1) ◽  
Author(s):  
Sergei Gennadievich Tankeev
Keyword(s):  
Abelian Varieties ◽  
3 Dimensional ◽  
Neron Models ◽  
Néron Models

scholarly journals The Manin constant in the semistable case

2018 ◽  
Vol 154 (9) ◽  
pp. 1889-1920 ◽  
Author(s):  
Kęstutis Česnavičius
Keyword(s):  
Vector Space ◽  
Elliptic Curve ◽  
Abelian Varieties ◽  
Higher Dimensional ◽  
Special Cases ◽  
Modular Parametrization ◽  
De Rham ◽  
Neron Models ◽  
General Relations ◽  
Néron Models

For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured the agreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space $H^{0}(E,\unicode[STIX]{x1D6FA}^{1})$. Multiple authors generalized his conjecture to higher-dimensional newform quotients. We prove the Manin conjecture for semistable $E$, give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral $p$-adic étale and de Rham cohomologies of abelian varieties over $p$-adic fields and exhibit a new exactness result for Néron models.

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.

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

scholarly journals Néron Models and Formal Groups

2008 ◽  
Vol 76 (1) ◽  
pp. 93-123 ◽  
Author(s):  
Gerd Faltings
Keyword(s):  
Formal Groups ◽  
Neron Models ◽  
Néron Models

Formal Néron models and Weil restriction

2000 ◽  
Vol 316 (3) ◽  
pp. 437-463 ◽  
Author(s):  
Alessandra Bertapelle
Keyword(s):  
Weil Restriction ◽  
Neron Models ◽  
Néron Models
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