Positivity of Hodge bundles of abelian varieties over some function fields

DOI10.1112/S0010437X21007430OpenAlexW3191553894MaRDI QIDQ5009394

Xinyi Yuan

Publication date: 23 August 2021

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03960

zbMATH Keywords

heightfunction fieldNéron modelTate-Shafarevich groupample vector bundletorsorsBSD conjectureabelian schemeTate conjectureHodge bundlepurely inseparable points

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Global ground fields in algebraic geometry (14G25) Positive characteristic ground fields in algebraic geometry (14G17)

Related Items (2)

Perfect points on curves of genus 1 and consequences for supersingular K3 surfaces ⋮ Perfect points of abelian varieties

Cites Work

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• The Tate conjecture for \(K3\) surfaces over finite fields
• Supersingular \(K3\) surfaces for large primes. With an Appendix by Andrew Snowden.
• The Tate conjecture for \(K3\) surfaces in odd characteristic
• The Tate conjecture for ordinary K 3 surfaces over finite fields
• Finiteness theorems for abelian varieties over number fields.
• Tate's conjecture for \(K3\) surfaces of finite height
• On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristic \(p>0\)
• On a conjecture of Artin and Tate
• Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic. -- Erratum
• Purely inseparable points on curves of higher genus
• On the conjectures of Birch and Swinnerton-Dyer in characteristic \(p>0\)
• Newton polygons and formal groups: Conjectures by Manin and Grothendieck
• Zur Vermutung von Birch und Swinnerton-Dyer über globalen Funktionenkoerpern
• The Shafarevich-Tate conjecture for pencils of elliptic curves on K3 surfaces
• Semistable sheaves in positive characteristic
• Projective regular models for abelian varieties, semistable reduction, and the height pairing
• A variational Tate conjecture in crystalline cohomology
• On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic. II
• On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic
• Chow's \(K/k\)-image and \(K/k\)-trace, and the Lang-Néron theorem
• Monodromy of Hecke-invariant subvarieties
• Endomorphisms of Abelian varieties over finite fields
• The Tate-*Safarevic group of a constant abelian variety
• Ample vector bundles
• Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux. Exposés VIII à XVIII. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3) dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Subvarieties of moduli spaces
• Bertini theorems over finite fields
• The -parity conjecture for abelian varieties over function fields of characteristic
• Algebraic Groups
• A positive characteristic Manin–Mumford theorem
• Division points on subvarieties of isotrivial semi-abelian varieties
• Néron Models
• Curves and Jacobians over Function Fields
• Elliptic Curves over the Perfect Closure of a Function Field
• Elements of Order P in the Tate-šafarevič Group
• Ample Vector Bundles on Curves
• Tensor Products of Ample Vector Bundles in Characteristic p

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