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AAG (Arithmetic algebraic geometry)
Charp
See also Kato homology
Abstract of Geisser: We define an integral Borel-Moore homology theory over finite fields, called arithmetic homology, and an integral version of Kato homology. Both types of groups are expected to be finitely generated, and sit in a long exact sequence with higher Chow groups of zero-cycles.
nLab page on Arithmetic homology