X-Nico

Pierre Deligne

In joint work with George Lusztig, Deligne and Lusztig applied étale cohomology to construct representations of finite groups of Lie type; with Michael Rapoport, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms.

Topos

For instance, there is an example due to Pierre Deligne of a nontrivial topos that has no points (see below for the definition of points of a topos).

Nagata's compactification theorem

Deligne showed, in unpublished notes expounded by Conrad, that the condition that S is Noetherian can be replaced by the condition that S is quasi-compact and quasi-separated.

see also