PulseExploreJournal ClubResearchersJournals
Instagram
HomeJournal ClubExplore
Synapse
⌘+K
Synapse
August 14, 2026Journal of the Institute of Mathematics of JussieuOpen Access

Periods in Families and Derivatives of Period Maps

View Full Paper
Ask AI
Bookmark
Share

Authors

BBBen BakkerJPJonathan PilaJTJacob Tsimerman

Discussion

Loading...

Member takes

Overview

Theoretical analysis characterizes algebraic closures of period fields and determines transcendence degrees in flat vector bundles, generalizing foundational work by Bertrand and Zudilin.

Key Points

  • To investigate the algebraic properties of (quasi)-period functions from smooth proper algebraic families and determine transcendence degrees for general flat vector bundles.
  • Analyzed the function fields generated by fiberwise (quasi)-periods across the base space of smooth proper algebraic families.
  • Examined coordinate representations of Hodge filtrations on flag varieties along with their differential derivatives.
  • Generalized differential algebraic techniques to evaluate flat coordinates associated with algebraic sections of arbitrary flat vector bundles.
  • Proved that the field generated by family periods has the same algebraic closure as the field generated by Hodge filtration flag variety coordinates and their derivatives.
  • Determined the transcendence degree of function fields generated by the flat coordinates of algebraic sections in general flat vector bundles.

Cite This Study

Bakker et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912b73https://doi.org/10.1017/s1474748026101972
View Full Paper
Ask AI
Bookmark
Share