Bibliography

EGA V continues the EGA IV bibliography. The standing-abbreviation table from EGA IV is reproduced below and extended with three additional Séminaire Bourbaki exposés and Mumford's Lectures on curves on an algebraic surface, both of which are heavily cited in §V.5 and §V.6.

Standing abbreviations (inherited from EGA IV; extended)

Key in EGA V	Work
$(I, \dots)$	A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique : I, IHÉS 4 (1960).
$(II, \dots)$	Éléments de géométrie algébrique : II, IHÉS 8 (1961).
$(III, \dots)$	Éléments de géométrie algébrique : III, IHÉS 11 (1961), 17 (1963).
$(I V, \dots)$	Éléments de géométrie algébrique : IV, IHÉS 20 (1964), 24 (1965), 28 (1966), 32 (1967).
$(0_{III}, \dots)$	Running Chapter 0 of EGA III, §§8-13.
$(0_{I V}, \dots)$	Running Chapter 0 of EGA IV, §§14-23.
$(M, \dots)$	H. Cartan and S. Eilenberg, Homological Algebra (Princeton, 1956).
$(G, \dots)$	R. Godement, Topologie algébrique et théorie des faisceaux (Hermann, 1958).
$(T, \dots)$	A. Grothendieck, Sur quelques points d'algèbre homologique (Tôhoku Math. J., 1957).
$(F A C, \dots)$	J.-P. Serre, Faisceaux algébriques cohérents (Annals of Math., 1955).
`(Bourbaki, Alg. comm., …)`	N. Bourbaki, Éléments de mathématique : Algèbre commutative (Hermann, 1961-1965).
$(B o u r baki, A l g ., \dots)$	N. Bourbaki, Éléments de mathématique : Algèbre (Hermann, 1942-).
$(B o u r baki, T o p . g \overset{e}{ˊ} n ., \dots)$	N. Bourbaki, Éléments de mathématique : Topologie générale (Hermann, 1940-).
$(N a g a t a, \dots)$	M. Nagata, Local Rings (Interscience, 1962).
$(Z a r i s ki - S am u e l, \dots)$	O. Zariski and P. Samuel, Commutative Algebra (Van Nostrand, 1958-1960).
$(M u m f or d, \dots)$	D. Mumford, Lectures on curves on an algebraic surface (Princeton Math. Notes 59, 1966).
$(B o u r baki S \overset{e}{ˊ} m .232)$	A. Grothendieck, Techniques de construction en géométrie analytique, Sém. Bourbaki, exposé 232 (Février 1962).
$(B o u r baki S \overset{e}{ˊ} m .236)$	A. Grothendieck, Techniques de descente et théorèmes d'existence en géométrie algébrique, Sém. Bourbaki, exposés 190, 195, 212, 221, 232, 236 (1959-62).
$(B o u r baki S \overset{e}{ˊ} m .261)$	A. Grothendieck, Techniques de construction de schémas, Sém. Bourbaki, exposé 261 (Mai 1963).

The Bourbaki references appearing in the text take the form (Bourbaki, Alg. comm., chap. II, §3, n° 4) or the shorter (Bourbaki, Alg. comm., II, §3, n° 4). Page numbers are kept when present.

Entries referenced in EGA V

This list extends the EGA IV bibliography (entries [1]-[44]). New entries [45]-[52] are introduced by EGA V; the numbering continues the sequence used through EGA I-IV. Entries already in EGA IV (e.g. Bourbaki's Algèbre commutative, Nagata's Local Rings, Mumford-Tate, Serre's Faisceaux algébriques cohérents) are not re-listed here; their numbers in the EGA III/IV bibliographies remain authoritative.

[45] D. Mumford, Lectures on curves on an algebraic surface, Princeton Mathematical Notes 59, Princeton University Press, 1966.

[46] A. Grothendieck, Techniques de construction en géométrie analytique, Séminaire H. Cartan, 13e année: 1960/61, exposés 7-17, École Normale Supérieure, 1962. (Cited as Sém. Bourbaki exposé 232 in some places; see also [47].)

[47] A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique, six Séminaire Bourbaki exposés (190 — December 1959; 195 — May 1960; 212 — February 1961; 221 — May 1961; 232 — February 1962; 236 — May 1962), reprinted in Fondements de la Géométrie Algébrique (FGA), Secrétariat Mathématique, Paris, 1962. (Often cited collectively as the "FGA descent theorems".)

[48] A. Grothendieck, Techniques de construction de schémas (Sém. Bourbaki, exposé 261, Mai 1963), reprinted in FGA.

[49] A. Seidenberg, The hyperplane sections of normal varieties, Trans. Amer. Math. Soc. 69 (1950), pp. 357-386. — Cited in §V.5.5 ("Seidenberg-style theorems").

[50] O. Zariski, The theorem of Bertini on the variable singular points of a linear system of varieties, Trans. Amer. Math. Soc. 56 (1944), pp. 130-140. — Cited at §V.5.3 (Bertini-Zariski theorem).

[51] M. Artin, Elementary morphisms and Henselization, several Séminaire Bourbaki and Harvard preprints, 1962-1968. — Cited in the §V.5.13 sommaire entry ("Elementary morphisms and a theorem of M. Artin"), though no full prenote of §V.5.13 survives.

[52] J.-P. Serre, Espaces fibrés algébriques, Séminaire C. Chevalley, 3e année: 1958, exposé 1, Secrétariat Mathématique, Paris, 1958. — Cited in §V.6.1 for the Picard-group computation of projective fibrations.

Translator's note

The EGA V prenotes also reference work by Hironaka, Nagata, Serre (beyond (FAC) and [52]), Chevalley, and others. Most of these references appear without precise pagination in the prenotes (Grothendieck's notes-to-self typically abbreviate to author surname and the result invoked). Where the specific result is cited in the prenote, we trace it to the EGA III/IV bibliographic entry; where the prenote leaves the reference vague, we preserve that vagueness in the translated body and add a translator footnote only if the modern equivalent is non-obvious.

The Vaiello unified edition ( $p a p ers / b oo k s / e g a / v /04 - v ai e ll o - u ni f i e d - t r an s l a t i o n . m d$ ) is the operational source for §§V.2.15-2.16 and is consulted as a reconciliation reference for §§V.1, V.5, V.6 when the Blass piecemeal source has ambiguous or illegible passages. The Vaiello edition itself is not bibliographically citable as a separate work; the underlying translations are by Piotr Blass and Joseph Blass.

Éléments de Géométrie Algébrique — English

Bibliography

Standing abbreviations (inherited from EGA IV; extended)

Entries referenced in EGA V

Translator's note