Anabelian geometry and descent obstructions on moduli spaces

Type of content
Journal Article
Thesis discipline
Degree name
Publisher
MATHEMATICAL SCIENCE PUBL
Journal Title
Journal ISSN
Volume Title
Language
English
Date
2016
Authors
Patrikis S
Voloch JF
Zarhin YG
Abstract

We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties and of curves over number fields. For the former we show that the section conjecture fails and the finite descent obstruction holds for a general class of adelic points, assuming several well-known conjectures. This is done by relating the problem to a local-global principle for Galois representations. For the latter, we show how the sufficiency of the finite descent obstruction implies the same for all hyperbolic curves.

Description
Citation
Patrikis S, Voloch JF, Zarhin YG (2016). Anabelian geometry and descent obstructions on moduli spaces. Algebra and Number Theory. 10(6). 1191-1219.
Keywords
Science & Technology, Physical Sciences, Mathematics, Anabelian geometry, moduli spaces, abelian varieties, descent obstruction, ABELIAN-VARIETIES, NUMBER-FIELDS, GALOIS ACTION, CURVES, REDUCTION, POINTS, ENDOMORPHISMS, FINITENESS, THEOREM
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theory
Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometry
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