The Grothendieck-Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and loosely analogous to the Chebotarev density theorem considered as a polynomial case. It is a conjecture of Alexander Grothendieck from the late 1960s, apparently never published by him in any form. The general case remains unsolved despite recent progress, and it has been linked to geometric investigations involving algebraic foliations. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Proposed Year Progress Toward ResolutionThe general case remains unsolved despite recent progress; a wide class of cases was proved by Benson Farb and Mark Kisin for equations on a locally symmetric variety. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
Sources
1. Grothendieck-Katz p-curvature Conjecture (Wikipedia)
Wikimedia FoundationLead section
It is a conjecture of Alexander Grothendieck from the late 1960s, and apparently not published by him in any form.
History section
Grothendieck put it forth in public discussion in Spring 1969, but wrote nothing on the topic.
Progress section
The general case remains unsolved, despite recent progress.
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