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- Q4682344 subject Q8234760.
- Q4682344 abstract "In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the category of pure motives with respect to that relation.Possible (and useful) adequate equivalence relations include rational, algebraic, homological and numerical equivalence. They are called "adequate" because dividing out by the equivalence relation is functorial, i.e. push-forward (with change of co-dimension) and pull-back of cycles is well-defined. Codimension one cycles modulo rational equivalence form the classical group of divisors. All cycles modulo rational equivalence form the Chow ring.".
- Q4682344 wikiPageWikiLink Q130998.
- Q4682344 wikiPageWikiLink Q1322856.
- Q4682344 wikiPageWikiLink Q1384888.
- Q4682344 wikiPageWikiLink Q15176852.
- Q4682344 wikiPageWikiLink Q161973.
- Q4682344 wikiPageWikiLink Q180969.
- Q4682344 wikiPageWikiLink Q18815110.
- Q4682344 wikiPageWikiLink Q3324325.
- Q4682344 wikiPageWikiLink Q3554818.
- Q4682344 wikiPageWikiLink Q395.
- Q4682344 wikiPageWikiLink Q4723996.
- Q4682344 wikiPageWikiLink Q5105491.
- Q4682344 wikiPageWikiLink Q5105523.
- Q4682344 wikiPageWikiLink Q7071450.
- Q4682344 wikiPageWikiLink Q7598336.
- Q4682344 wikiPageWikiLink Q764115.
- Q4682344 wikiPageWikiLink Q7980184.
- Q4682344 wikiPageWikiLink Q8234760.
- Q4682344 wikiPageWikiLink Q840594.
- Q4682344 wikiPageWikiLink Q909669.
- Q4682344 comment "In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives.".
- Q4682344 label "Adequate equivalence relation".