% The sources of the library: its one bibliography.
%
% The key of an entry is the key by which everything cites the source: the docstrings and
% comments ([Hir64, Main Theorem I], [Wlo05, §4.6]), among them the paragraphs
% `Source statement: [KEY, locator, page]` of the theorems that formalize an item of a source, the
% blueprint and the Markdown files. Item numbers in citations
% ([Kol07, Theorem 68]) are the source's own. 
%
% What reads this file:
% - scripts/sync_formalization.lean checks that each `Source statement:` paragraph cites a key of
%   this file, and writes the key as the authors' last names and the year ("Hironaka 1964") in the
%   alignment table of formalization.yaml.
% - blueprint/Blueprint/References.lean registers every entry for the blueprint's citations
%   ({cite Hir64}[Main Theorem I] in the chapters, [Hir64, Main Theorem I] in the annotation items
%   taken from docstrings) and its bibliography, which lists the entries the blueprint cites.
% - scripts/check_references.py checks that a source is listed here exactly when some file of the
%   package cites it.
% - scripts/check_formalization_yaml.py compares the sources of formalization.yaml with the
%   entries of the same title (and their authors).
% - scripts/build_docs.py gives this file to doc-gen4 for the bibliography of the API
%   documentation (doc-gen4 reads only ASCII keys, so the script stands in for the others).
%
% To add a source: add its entry here and cite it (the check fails on an entry that nothing
% cites). To drop a source, delete its entry with its last citation.
%
% The file is written in the part of BibTeX that all of these read: an entry is
% `type{key, field = {value}, ...}` after the at sign, a value is in braces or is a bare number,
% accented letters are written as Unicode characters (no TeX macros), and braces protect
% capitals in titles. These comments go between entries, on lines starting with a percent sign,
% and never contain the at sign, which starts an entry.

% Resolution of singularities: the sources followed

@Article{Hir64,
  author = {Hironaka, Heisuke},
  title = {Resolution of singularities of an algebraic variety over a field of characteristic zero. {I}, {II}},
  journal = {Annals of Mathematics (2)},
  volume = {79},
  year = {1964},
  pages = {109--203 and 205--326},
  doi = {10.2307/1970486},
  note = {Part II: doi:10.2307/1970547}
}

% Kol07: the text consulted is the arXiv version of Chapter 3, and item numbers follow it; the url
% field points to that version.
@Book{Kol07,
  author = {Kollár, János},
  title = {Lectures on Resolution of Singularities},
  series = {Annals of Mathematics Studies},
  volume = {166},
  publisher = {Princeton University Press},
  year = {2007},
  eprint = {math/0508332},
  archiveprefix = {arXiv},
  url = {https://arxiv.org/abs/math/0508332v3},
  note = {The arXiv text (v3) is the resolution chapter, circulated as a Seattle lecture; item numbers follow it}
}

% Wlo05: the arXiv version is v1 (2004).
@Article{Wlo05,
  author = {Włodarczyk, Jarosław},
  title = {Simple {H}ironaka resolution in characteristic zero},
  journal = {Journal of the American Mathematical Society},
  volume = {18},
  year = {2005},
  pages = {779--822},
  doi = {10.1090/S0894-0347-05-00493-5},
  eprint = {math/0401401},
  archiveprefix = {arXiv}
}

@InProceedings{Wlo09,
  author = {Włodarczyk, Jarosław},
  title = {Resolution of singularities of analytic spaces},
  booktitle = {Proceedings of the 15th {G}ökova Geometry--Topology Conference (2008)},
  publisher = {International Press},
  year = {2009},
  pages = {31--63},
  url = {https://gokovagt.org/proceedings/2008/ggt08-wlodarczyk.pdf}
}

@Article{BM88,
  author = {Bierstone, Edward and Milman, Pierre D.},
  title = {Semianalytic and subanalytic sets},
  journal = {Publications Mathématiques de l'IHÉS},
  volume = {67},
  year = {1988},
  pages = {5--42},
  doi = {10.1007/BF02699126}
}

% BM97: only Chapter I, the arXiv text, was consulted, and item numbers follow it; the url field
% points to it.
@Article{BM97,
  author = {Bierstone, Edward and Milman, Pierre D.},
  title = {Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant},
  journal = {Inventiones Mathematicae},
  volume = {128},
  year = {1997},
  pages = {207--302},
  doi = {10.1007/s002220050141},
  eprint = {alg-geom/9508005},
  archiveprefix = {arXiv},
  url = {https://arxiv.org/abs/alg-geom/9508005},
  note = {Item numbers follow the arXiv version}
}

% BM08: the arXiv version is v1 (2007).
@Article{BM08,
  author = {Bierstone, Edward and Milman, Pierre D.},
  title = {Functoriality in resolution of singularities},
  journal = {Publications of the Research Institute for Mathematical Sciences},
  volume = {44},
  year = {2008},
  pages = {609--639},
  doi = {10.2977/prims/1210167338},
  eprint = {math/0702375},
  archiveprefix = {arXiv}
}

@Article{Hau03,
  author = {Hauser, Herwig},
  title = {The {H}ironaka theorem on resolution of singularities (or: {A} proof we always wanted to understand)},
  journal = {Bulletin of the American Mathematical Society},
  volume = {40},
  year = {2003},
  pages = {323--403},
  doi = {10.1090/S0273-0979-03-00982-0}
}

% Hau14: the arXiv version is v1 (2014).
@InCollection{Hau14,
  author = {Hauser, Herwig},
  title = {Blowups and resolution},
  booktitle = {The Resolution of Singular Algebraic Varieties},
  series = {Clay Mathematics Proceedings},
  volume = {20},
  publisher = {American Mathematical Society},
  year = {2014},
  pages = {1--80},
  eprint = {1404.1041},
  archiveprefix = {arXiv},
  url = {https://arxiv.org/abs/1404.1041}
}

% Sta: cited by tag, [Sta, Tag 00TT]; the tags are the project's permanent identifiers.
@Misc{Sta,
  author = {{The Stacks Project Authors}},
  title = {The {S}tacks {P}roject},
  note = {Cited by tag},
  url = {https://stacks.math.columbia.edu}
}

% Ati70: the Resolution Theorem, the local monomialization of a real-analytic function, which

% Atiyah derives from Hironaka's theorem for the division of distributions.

@Article{Ati70,
  author = {Atiyah, Michael F.},
  title = {Resolution of singularities and division of distributions},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {23},
  number = {2},
  year = {1970},
  pages = {145--150},
  doi = {10.1002/cpa.3160230202}
}

% BG69: Lemma 1, the monomialization of a regular function on a real algebraic manifold, which

% Bernstein and Gelfand derive from Hironaka's theorem for the meromorphic continuation of P^λ.

@Article{BG69,
  author = {Bernshtein, I. N. and Gel'fand, S. I.},
  title = {Meromorphic property of the functions {P}^λ},
  journal = {Functional Analysis and Its Applications},
  volume = {3},
  number = {1},
  year = {1969},
  pages = {68--69},
  doi = {10.1007/BF01078276}
}

% Analytic geometry and analysis

@Book{GR65,
  author = {Gunning, Robert C. and Rossi, Hugo},
  title = {Analytic Functions of Several Complex Variables},
  publisher = {Prentice-Hall},
  year = {1965},
  note = {Reprinted, AMS Chelsea Publishing, 2009},
  doi = {10.1090/chel/368}
}

@Book{GR71,
  author = {Grauert, Hans and Remmert, Reinhold},
  title = {Analytische {S}tellenalgebren},
  series = {Grundlehren der mathematischen Wissenschaften},
  volume = {176},
  publisher = {Springer},
  year = {1971},
  doi = {10.1007/978-3-642-65033-8}
}

@Book{GR84,
  author = {Grauert, Hans and Remmert, Reinhold},
  title = {Coherent Analytic Sheaves},
  series = {Grundlehren der mathematischen Wissenschaften},
  volume = {265},
  publisher = {Springer},
  year = {1984},
  doi = {10.1007/978-3-642-69582-7}
}

@Book{Nar66,
  author = {Narasimhan, Raghavan},
  title = {Introduction to the Theory of Analytic Spaces},
  series = {Lecture Notes in Mathematics},
  volume = {25},
  publisher = {Springer},
  year = {1966},
  doi = {10.1007/BFb0077071}
}

@Misc{Fre17,
  author = {Freitag, Eberhard},
  title = {Complex Spaces},
  howpublished = {Lecture notes, Universität Heidelberg},
  year = {2017},
  url = {https://www.mathi.uni-heidelberg.de/~freitag/skripten/complexspaces.pdf}
}

@Article{BW59,
  author = {Bruhat, François and Whitney, Hassler},
  title = {Quelques propriétés fondamentales des ensembles analytiques-réels},
  journal = {Commentarii Mathematici Helvetici},
  volume = {33},
  year = {1959},
  pages = {132--160},
  doi = {10.1007/BF02565913}
}

@Article{Car57,
  author = {Cartan, Henri},
  title = {Variétés analytiques réelles et variétés analytiques complexes},
  journal = {Bulletin de la Société Mathématique de France},
  volume = {85},
  year = {1957},
  pages = {77--99},
  doi = {10.24033/bsmf.1481}
}

@Book{Dem,
  author = {Demailly, Jean-Pierre},
  title = {Complex Analytic and Differential Geometry},
  publisher = {Université de Grenoble I},
  year = {2012},
  note = {Online book, version of 2012},
  url = {https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf}
}

% Algebraic geometry and commutative algebra

@Book{Har77,
  author = {Hartshorne, Robin},
  title = {Algebraic Geometry},
  series = {Graduate Texts in Mathematics},
  volume = {52},
  publisher = {Springer},
  year = {1977},
  doi = {10.1007/978-1-4757-3849-0}
}

@Book{Mat89,
  author = {Matsumura, Hideyuki},
  title = {Commutative Ring Theory},
  series = {Cambridge Studies in Advanced Mathematics},
  volume = {8},
  publisher = {Cambridge University Press},
  year = {1989},
  doi = {10.1017/CBO9781139171762}
}

@Book{AM69,
  author = {Atiyah, Michael F. and Macdonald, Ian G.},
  title = {Introduction to Commutative Algebra},
  publisher = {Addison-Wesley},
  year = {1969}
}

@Book{Wat09,
  author = {Watanabe, Sumio},
  title = {Algebraic Geometry and Statistical Learning Theory},
  series = {Cambridge Monographs on Applied and Computational Mathematics},
  volume = {25},
  publisher = {Cambridge University Press},
  year = {2009},
  doi = {10.1017/CBO9780511800474}
}