Tropical Corrections to P equals W on Mumford Curves

Definitions and mathematical statement

The notation $P=W$ conventionally refers to a comparison between a perverse filtration $P$ and a weight filtration $W$ on suitable cohomological objects. Such a comparison requires specified spaces, cohomology theories, filtrations, an identification between the relevant objects, and indexing conventions. None of these data, nor a definition of a tropical correction, is provided in the supplied passage.

A Mumford curve ordinarily means a smooth proper curve over a non-Archimedean field with totally degenerate reduction. This terminology provides context only: the supplied record does not specify a base field, genus, reduction convention, or associated geometric construction on which the proposed filtrations would be defined.

Does a $P=W$ phenomenon with a tropical correction occur in other non-Archimedean settings, such as Mumford curves?

This is the research question supplied by the record. The original wording asks for a phenomenon similar to one in preceding report context, but that preceding mathematical construction is not included. Consequently, the question cannot yet be expressed as a definite equality of filtrations or a quantified existence statement for a specified correction. In particular, no universal assertion over Mumford curves, filtration-index conversion, or formula for the correction is asserted here.

Short English statement

The supplied question asks whether a tropical correction makes a $P=W$ comparison possible in further non-Archimedean settings, with Mumford curves given as an example. The relevant spaces, filtrations, comparison, and correction are unspecified, so this remains a research question requiring mathematical clarification.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30005535$, titled Tropical Corrections to P equals W on Mumford Curves; exact source problem code catalogue entry. Collection: Oberwolfach Reports Open Problems. The record gives proposed year 2023 and names no individual proposer.
• Supplied report attribution: Tropical Methods in Geometry (2023), Oberwolfach Reports, pp. 1263--1322, DOI 10.4171/owr/2023/23. https://doi.org/10.4171/owr/2023/23. The supplied passage attributes the question to the report's discussion; it gives no precise page or speaker for this question.
• Supplied literature source, labeled "OWR 2023 23": https://ems.press/content/serial-article-files/47020.
• Supplied literature source, labeled "P equals W for abelian varieties": https://arxiv.org/abs/2303.03734.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the problem open and states that the report asks about a tropical correction to $P=W$ for Mumford curves and that no proof of such a phenomenon was found. This is supplied dated curation, not an independently verified literature assessment. The background explicitly calls for independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and reports that the official report was checked directly and that definitions were restored. These are supplied provenance claims; the provided statement and passage still omit the mathematical data needed for a precise filtration comparison. No independent source consultation is claimed here.