Paper040_The_Fintzen_Piccirillo_Lock.
Fuente:
Zenodo
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Pubblicazione: |
Zenodo
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901059170992128 |
|---|---|
| author | Pompetzki, Christopher |
| author_facet | Pompetzki, Christopher |
| contents | <p>We prove that the combined output of Lisa Piccirillo (22 papers on low-dimensional topology) and Jessica Fintzen (20 papers on <em>p</em>-adic representation theory) reduces, without remainder, to iterated applications of the rank-nullity theorem on finite-dimensional vector spaces equipped with flags.</p> <p>Piccirillo's papers compute ker ∂ / im ∂ for nilpotent operators ∂ on face lattices of CW complexes. Fintzen's papers compute eigenspaces of semisimple operators on filtration lattices of <em>p</em>-adic groups.</p> <p>These are the two halves of the Jordan–Chevalley decomposition <em>T</em> = <em>S</em> + <em>N</em> applied to the associated graded of a finite flag. Piccirillo works in the nilpotent sector (<em>S</em> = 0, solve for <em>N</em>). Fintzen works in the semisimple sector (quotient out <em>N</em>, solve for <em>S</em>). Both use four operations: rank, ker, tr, <em>N<sup>k</sup></em> = 0.</p> <p>The reduction is organized as a paper-by-paper translation into the language of the Lattice Spectral Classification Theorem (Paper 10 of this series). Everything else is notation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18787142 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper040_The_Fintzen_Piccirillo_Lock. Pompetzki, Christopher Linear algebra <p>We prove that the combined output of Lisa Piccirillo (22 papers on low-dimensional topology) and Jessica Fintzen (20 papers on <em>p</em>-adic representation theory) reduces, without remainder, to iterated applications of the rank-nullity theorem on finite-dimensional vector spaces equipped with flags.</p> <p>Piccirillo's papers compute ker ∂ / im ∂ for nilpotent operators ∂ on face lattices of CW complexes. Fintzen's papers compute eigenspaces of semisimple operators on filtration lattices of <em>p</em>-adic groups.</p> <p>These are the two halves of the Jordan–Chevalley decomposition <em>T</em> = <em>S</em> + <em>N</em> applied to the associated graded of a finite flag. Piccirillo works in the nilpotent sector (<em>S</em> = 0, solve for <em>N</em>). Fintzen works in the semisimple sector (quotient out <em>N</em>, solve for <em>S</em>). Both use four operations: rank, ker, tr, <em>N<sup>k</sup></em> = 0.</p> <p>The reduction is organized as a paper-by-paper translation into the language of the Lattice Spectral Classification Theorem (Paper 10 of this series). Everything else is notation.</p> |
| title | Paper040_The_Fintzen_Piccirillo_Lock. |
| topic | Linear algebra |
| url | https://doi.org/10.5281/zenodo.18787142 |