UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answe...

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Veröffentlicht in:Forum of mathematics. Sigma 2018-01, Vol.6, Article e13
Hauptverfasser: SHANKAR, ANANTH N., TSIMERMAN, JACOB
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Fields (mathematics)
Intersections
Number Theory
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Zusammenfassung:We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2018.15