Cohomological Finite-Generation Survey Summary

Definitions and mathematical statement

The supplied record concerns finite generation of the cohomology of finite group schemes over Verlinde categories. Its substantive content is a description of a talk presenting recent results and related open questions. It supplies no standalone mathematical question, conjecture, or theorem to formalize.

In particular, the record does not specify the base field or its characteristic, the Verlinde categories under consideration, the definition of a finite group scheme over such a category, the cohomology theory and coefficients, or the intended meaning of finite generation. It also gives no hypotheses or quantifiers identifying the objects to which an asserted finite-generation property should apply. These definitions and qualifications cannot be recovered from the supplied passage.

The supplied statement status is unrecoverable, and no clean statement is supplied. Consequently, no precise finite-generation assertion can be stated from this evidence. This entry preserves the survey topic and the unresolved formulation issues; it does not formulate a universal finite-generation conjecture. The registry label open is supplied curation, not an independently verified mathematical conclusion.

Short English statement

This record summarizes a survey on cohomological finite generation for finite group schemes over Verlinde categories. The supplied passage contains no specific open problem and lacks the definitions, hypotheses, and quantifiers needed for a precise statement. Recovery of an intended question requires further source evidence and human mathematical review.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30006645$, titled Cohomological Finite-Generation Survey Summary; exact source problem code catalogue entry, in the collection Oberwolfach Reports Open Problems. The record gives the proposed year as 2026 and names no proposer.
• Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, pp. 541--610, DOI 10.4171/owr/2026/9: https://doi.org/10.4171/owr/2026/9. The extracted passage includes a page marker for p. 543. This is also the supplied literature source labelled "originating Oberwolfach report."
• Notes on Cohomological Finite Generation for Finite Group Schemes: https://arxiv.org/abs/2510.02908. This reference is supplied in the literature-source list; no authors or specific supporting result are supplied.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the topic open and describes the record as a programmatic account of recent results and open questions, rather than a resolved finite-generation theorem. It states that the general problem remains active. This is supplied dated curation, not independently verified; the record itself requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification note reports that the official report confirms the extraction is a programmatic survey summary without a standalone open problem. It states that no separate clean statement is promoted and that the original record is retained publicly for provenance. This verification claim is reproduced as supplied and was not independently checked.