Arithmetic Kashiwara conjecture of Esnault and Kerz
The unrestricted Arithmetic Kashiwara conjecture of Esnault--Kerz asserts the corresponding arithmetic Kashiwara statement for general arithmetic bases, beyond the case of geometric traits in equicharacteristic. The supplied sources do not state its full hypotheses and conclusion precisely.
References
Primary source
Additional references
- Spreading out perverse sheaves — arXiv — Beat Zurbuchen
Progress summary
A new unrefereed result proves only a restricted equal-characteristic version, so the full conjecture remains open.
The Arithmetic Kashiwara conjecture of Esnault and Kerz concerns arithmetic Kashiwara-type and decomposition statements. The latest report gives a result for geometric traits in equicharacteristic, rather than the unrestricted conjecture.
October 2026 restricted-case result
On October 5, 2026, Beat Zurbuchen reported constructing relatively perverse universally locally acyclic extensions over dense opens and applying them to prove the conjecture for geometric traits in equicharacteristic. This extends the known range but is explicitly unrefereed and does not settle the general arithmetic conjecture.
Current status (as of October 2026): The geometric-trait equicharacteristic case is claimed, but the unrestricted Arithmetic Kashiwara conjecture remains open and the claim is unverified.
Sources
- arxiv.org
- claymath.org
- annals.math.princeton.edu
- sites.math.rutgers.edu
- comptes-rendus.academie-sciences.fr
- arxiv.org
- ncatlab.org
- researchgate.net
- kurims.kyoto-u.ac.jp
- ar5iv.labs.arxiv.org
- arxiv.org
- arxiv.org
- ar5iv.labs.arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
Solutions 0
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