Timeline for Has Grothendieck's motivic vision been realised?
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5 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2023 at 22:31 | comment | added | Timothy Chow | Arguably, a necessary condition for the completion of a "full theory of motives" would be someone claiming the million dollars for the Hodge conjecture. | |
| Mar 13, 2023 at 12:08 | comment | added | Donu Arapura | The methods of Voevodsky (and others) produce a triangulated category, which is morally the derived category of an abelian category of mixed motives. However, we don't actually know how to construct to constructed a t-structure with good properties etc. This is related to the standard conjectures mentioned above. So yeah the subject is very far from done. | |
| Mar 13, 2023 at 10:47 | comment | added | Philippe Gaucher | chatGPT provides a different answer : "Yes, mathematicians take Grothendieck's theory of "motives" very seriously. In fact, the theory of motives is one of the most active areas of research in algebraic geometry and number theory today. (...)" | |
| Mar 13, 2023 at 8:34 | comment | added | Boaz Moerman | There are still a number of basic conjectures by Grothendieck related to motives which are still unproven, such as his standard conjectures, as well as his conjecture on periods. | |
| Mar 13, 2023 at 8:26 | history | asked | Neil Strickland | CC BY-SA 4.0 |