nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqaufa4k (nprofile…fa4k) There are some algebraic geometers that study varieties in a similar way to the way you mention. Their approach works by noting that the derived category of quasicoherent sheaves on a scheme holds quite a lot of important geometric information. I think there are conjectures that it is a birational invariant even, but I am not certain since I don't recall the details.
This derived category has some nice structure that you can exploit in the case for projective spaces. For instance, you can pick a generating object (known as a tilting object) for the entire category. You can then use representation theory of other objects like quivers to gain a handle on those kinds of objects. Quivers are particularly nice because they have well understood moduli spaces of representations which make them suitable as a "presentation" of a derived category.
I asked a question about this on MO a while ago: https://mathoverflow.net/questions/285955/why-are-coherent-sheaves-on-bbb-p1-derived-equivalent-to-representations-of
I wonder if the POV with 2-rigs is in some way related to this. It has been a while since I've done AG however, so perhaps the relation is superficial at best.
Ali Caglayan /
npub10g…86ckt
2025-01-12 12:30:37
in reply to nevent1q…2m72
Author Public Key
npub10gn0h0k2f6qxgyzy8wsvverluutu7ktzzj4929zt0dxur5md78wsj86cktPublished at
2025-01-12 12:30:37Event JSON
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