Timeline for Definition of Motivic cohomology via Ext
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| Feb 7, 2023 at 9:57 | comment | added | D.-C. Cisinski | We expect that taking the dual is exact and induces an equivalence from mixed motives to the opposite category of mixed motives. The two definitions are related formally the same we go from singular homology to singular cohomology. The conventions are also related to the way you construct motives associated to algebraic varieties. Beilinson thought of this as a cohomology (hence contravariant) whereas Voevodsky considered this as homology. Therefore, both definitions agree, at least if you think of motivic cohomology as a cohomology of algebraic varieties. | |
| Feb 3, 2023 at 16:10 | history | asked | curious math guy | CC BY-SA 4.0 |