Resolution of Singularities in Positive Characteristic: Frobenius-Hasse Towers and Exceptional-History Descent

Key points

• It replaces marked Rees algebras with their differential-integral saturations and constructs total Hasse operators, coefficient cubes, and filtered Rees complexes, incorporating information into the local theory that numerical order alone misses in positive characteristic.
• It records transformations under admissible ordinary blowups through semilinear Frobenius-Hasse sources and finite exceptional genealogies, routes local defects through a six-line ledger to dedicated procedures for surfaces, toroidal-monomial, binomial, and additive cases, and then assembles their results into a single global ordering.
• The central mechanism is a global replacement certificate that transfers owner, parent, quotient, trace, and resumption information between macroblocks; for a complete state equipped with this certificate, it claims that iteration terminates because multisets strictly decrease under a single well-ordered dependency ordering.
• From this, it claims strong principalization of coherent ideals on smooth finite-type schemes over a perfect field k, making each ideal generated by one element, in Part IX, Theorem 15.3, and resolution preserving an ordered simple-normal-crossings boundary at every step; it states that the result is presentation-independent and functorial under re-embedding and étale pullback.
• However, this is a single-author v1 preprint spanning nine parts and 798 pages, classified on arXiv under General Mathematics (math.GM), so whether the proof actually holds can only be judged through peer review and independent verification.

Paper links

External research summaries. These are not HDATF publications or measured product results.