At the top of page 278 in Deligne's Weil I paper, he refers to the cohomology group $H_c^i(X,\mathcal{F})$ as having "support propre". This literally translates to "proper support", but in context it looks like it should be "compact support". Is that what "propre" means here?
2026-02-23 04:41:45.1771821705
What is the meaning of "support propre"?
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notice he has already used the adjective "propre" several times on pages 274 and 275 to refer to a property of a variety, ("propre et lisse"). since I believe a complex variety is compact (in the complex analytic topology) if and only if it is "complete" if and only if the map to the one point spectrum of the field is a proper map, I think you are right that he is using proper as a synonym for complete or compact.
See Mumford's redbook chapter I.10,Th. 2, and Hartshorne chapter II.4, definition top of p.105.