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Anonymous 2015-02-11 22:05:13 No.7062836

[Missing image file: ]

What are the established algebraic objects which come closest to motives?
Pic related is kinda what I imagine they look like?


>>
Anonymous 2015-02-11 22:51:25 No.7062949
>>7062836
Well cohomology (and especially etale cohomology ) is of course closely related.
Similar kinds of abstraction are Grothendieck's theories of schemes and topoi.
I've also heard the Grothendieck ring of varieties described as a "baby motivic theory."

Beyond this I don't really know anything and I welcome any anon who wants to jump in.

>>
Anonymous 2015-02-12 18:01:39 No.7064425
In algebraic geomety, it seems sheaves play a role twice - is that right?
On the one hand, they are what equips the (Zariski topological) spaces with their ring of of coordinate functions, but then the assignment of the algebraic structures, doing cohomolgy, is again formulated in terms of one? (Or was it a covariant functor?)







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