Authorship and component terms

The independently authored teaching, examples, exercise solutions and original figures by GPT-6.1 Sol (OpenAI), Codex, Ultra, use CC0 1.0.

Demailly and Siegel: preparation and division

The full germ-level preparation-and-division proof in Complex analytic spaces and analytification adapts Jean-Pierre Demailly’s Complex Analytic and Differential Geometry, 21 June 2012, II, Theorems2.1 and2.3, pp79–81. Demailly credits C. L. Siegel’s contour argument. It retains the author’s custom OpenContent permission to distribute and modify on the web while retaining authorship; this component is outside CC0. GPT-6.1 Sol reorganized the germ proof and made the unit case, root multiplicities, joint holomorphicity and uniqueness explicit. The additional uniform norm estimates are not included.

Stacks proof adaptations

The conductor and strong-transcendence appendix in The theorem on formal functions, the approximation appendix in Zariski connectedness and Stein factorization, and the adapted compact-generation, denominator, Brown, supported-factorization and duality constructions in The right adjoint of derived pushforward, retain the authorship of the Stacks project authors and the AI Integrated Stacks Project edition contributors. GPT-6.1 Sol (OpenAI), Codex, Ultra, wrote the adaptations and added arguments on 5 October 2026. These identified components are licensed under GFDL version 1.2 or any later version, with no Invariant Sections, no Front-Cover Texts and no Back-Cover Texts. A verbatim copy of the GNU Free Documentation License 1.2 accompanies the reader and editable archive. Independently authored portions retain their stated CC0 terms.

References and software

Linked AI Integrated Stacks Project texts retain GFDL1.2 and their authorship. MIT OpenCourseWare supplementary reading retains CC BY-NC-SA4.0. Other scholarly reading retains its own rights. Component record · MathJax Apache2.0 · Font notices.