Spectral spaces versus distributive lattices: a dictionary

Spectral spaces versus distributive lattices: a dictionary (pdf) arxiv/1812.06277
The file contains the English (slightly expanded) version, followed by a French translation.
p. 223--245 in: Advances in rings, modules and factorizations. Selected papers based on the presentations at the international conference on rings and factorizations, Graz, Austria, February 19--23, 2018. Cham: Springer (2020).

Abstract : The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and a short dictionary for this antiequivalence. We propose a translation of several abstract theorems (in classical mathematics) into constructive ones, even in the case where points of a spectral space have no clear constructive content.