Translation Ledger — SGA 4-I

This ledger records recurring translation choices for SGA 4-I. It is deliberately conservative: established English mathematical terminology is used where it exists, while historically loaded terms are not silently modernized.

Formatting

Source feature	English convention	Note
mathematical notation	TeX inside $...$ or `$$...$$`	Use KaTeX-friendly TeX, not Unicode mathematical glyphs.
arrows	`\to`, `\leftarrow`, `\Rightarrow`, `\Longleftrightarrow`	Avoid Unicode arrows in mathematics.
products and sums	`\prod`, `\coprod`, `\times`, `\times_X`	Use TeX operators rather than Unicode symbols.
limits	`\varprojlim`, `\varinjlim`, `\operatorname{colim}`	Preserve period terms “projective” and “inductive” in prose.
categories of presheaves/sheaves	`\widehat{C}`, `\widetilde{C}`	Use TeX instead of `C^` or `C~` when the symbol is mathematical.
universe notation	$U$ , $V$ , `$U$-site`, `$U$-small`	Keep source universe notation.
damaged diagrams	fenced `text` block with a translator warning	Do not silently reconstruct an uncertain OCR diagram.

Core Terminology

French	English	Note
topos	topos; plural topoi	Use `topoi` in prose. Keep `topos` in compounds such as “ringed topos”.
theorie des topos	theory of topoi	Title-level phrase.
site	site	Standard SGA terminology.
prefaisceau	presheaf	Standard.
faisceau	sheaf	Standard.
categorie	category	Standard.
foncteur	functor	Standard.
foncteur fibre	fiber functor	Standard; American spelling.
foncteur section	section functor	Standard for the SGA IV usage.
categorie des points d’un topos	category of points of a topos	Preserve the topos-theoretic sense.
point geometrique	geometric point	Standard.
morphisme de topos	morphism of topoi	Use plural “topoi” in the English compound.
morphisme de sites	morphism of sites	Standard.
topos annele	ringed topos	Standard.
topos localement annele	locally ringed topos	Standard.
espace annele	ringed space	Standard.
espace topologique	topological space	Standard.
espace a operateurs	space with operators	Historical/topological term; do not replace by “group action” unless the source does.
gros site / gros topos	big site / big topos	Standard English rendering.
petit	small	Size-theoretic term.
$U$ -petit	$U$ -small	Preserve universe notation.
univers	universe	Size-theoretic term.
cardinaux inaccessibles	inaccessible cardinals	Standard.
application	map	Use “function” only in elementary set-theoretic prose.
morphisme	morphism	Standard.
monomorphisme	monomorphism	Standard.
epimorphisme	epimorphism	Standard.
epimorphisme effectif	effective epimorphism	Standard.
epimorphisme strict	strict epimorphism	Historical categorical terminology; keep literal technical rendering.
epimorphique universelle	universally epimorphic	For families; “universal epimorphism” for a morphism when grammar calls for it.
bicouvrant	bicovering	Technical SGA IV term.
couvrant	covering	For sieves, morphisms, and families.
crible	sieve	Standard categorical topology term.
topologie	topology	Grothendieck topology unless the context is ordinary topology.
pretopologie	pretopology	Standard.
topologie canonique	canonical topology	Standard.
topologie grossiere	coarse topology	Historical source pairs it with chaotic topology.
topologie chaotique	chaotic topology	Preserve the source’s term.
recouvrement	covering	Prefer “covering” to “cover” in formal terminology.
raffinement	refinement	Standard.
categorie filtrante	filtered category	Standard.
categorie pseudo-filtrante	pseudo-filtered category	Preserve the source’s term.
limite projective	projective limit	Preserve period terminology in SGA IV; modern English often says “inverse limit”.
limite inductive	inductive limit	Preserve period terminology in SGA IV; modern English often says “direct limit”.
image directe	direct image	Standard for sheaves/topoi.
image inverse / image reciproque	inverse image	Standard.
prolongement par zero	extension by zero	Standard.
prolongement par le vide	extension by the empty object	Preserve the distinction from extension by zero.
recollement	gluing	Use “gluing”; “recollement” only if the term is used technically as such.
localisation	localization	Standard.
sous-topos	subtopos	Standard.
sous-topos ouvert / ferme / localement ferme	open / closed / locally closed subtopos	Standard.
plongement ouvert / ferme	open / closed embedding	Standard for topoi in this context.
adherence / interieur / exterieur / frontiere d’un sous-topos	closure / interior / exterior / boundary of a subtopos	Standard topological analogy.
support / cosupport	support / cosupport	Standard.
etendue	spread	Historical SGA IV term for topological spreads; use a note at first substantive occurrence.
sobre	sober	Topological term.
voisinage	neighborhood	American spelling.
generalisation / specialisation d’un point	generalization / specialization of a point	Standard.
stable par descente	stable under descent	Standard.
quarrable	quarrable	Preserve SGA’s historical term for “has representable base changes”; define at first substantive occurrence.
foncteur fibrant	fibering functor	SGA period terminology for a functor organized by cartesian pullbacks.
categorie fibre	fiber category	American spelling; preserve categorical sense.
filtration cardinale	cardinal filtration	Technical term of Expose I, § 9.
accessible / preaccessible	accessible / preaccessible	Preserve the exact size-theoretic distinction.
grand devant un cardinal	large relative to a cardinal	Literal size-theoretic term in the accessibility arguments.
foncteur ind-adjoint / pro-adjoint	ind-adjoint / pro-adjoint functor	Do not replace by modern adjoint functor terminology.
facteur direct	direct factor	For an image of an idempotent/projector.
projecteur	projector	Historical categorical/set-theoretic term for idempotent.
espece de structure	species of structure	Bourbaki terminology; do not paraphrase as “kind of structure”.
artinien	artinian	Lowercase in prose except at sentence start.
collectivisante	collectivizing	Bourbaki set-theoretic terminology.
torseur	torsor	Standard.
cohomologie a supports propres	cohomology with proper supports	Standard for $f_!$ context.
descente cohomologique	cohomological descent	Standard.
lissification	smoothification	Historical term; avoid paraphrase unless context demands.
coefficients de torsion premiers aux caracteristiques residuelles	torsion coefficients prime to the residual characteristics	Preserve exact hypothesis.
corps premier	prime field	Standard.
corps fini	finite field	Standard.

Proof and Expository Movement

French	English	Note
Soit / Soient	Let	Match singular/plural in English.
Supposons que	Suppose that / Assume	Choose by register.
On a	We have	Avoid repeated “one has” unless the impersonal style matters.
Il suffit de	It suffices to	Standard proof idiom.
Il reste a montrer	It remains to show	Standard proof idiom.
Il en resulte que	It follows that	Use “hence” only in compact proof prose.
Par suite	Consequently / hence	Choose by rhythm.
En effet	Indeed	Introduces justification.
D’ou	Hence	Use “whence” only when the register supports it.
A fortiori	A fortiori	Keep loan phrase; already idiomatic in mathematical English.

Notes Needing Review

The cleaned source flags the synoptic diagram of the second edition as too damaged for reliable transcription. The English front matter preserves that warning rather than inventing a reconstruction.
The notation index contains intentionally preserved uncertain OCR entries, such as (Karfiness) and Lib (Women’s Liberation). These should be checked against the PDF if they become mathematically relevant.

Keyboard shortcuts

Séminaire de Géométrie Algébrique du Bois-Marie — English

Translation Ledger — SGA 4-I

Formatting

Core Terminology

Proof and Expository Movement

Notes Needing Review