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41 votes
1 answer
3k views

Connes–Consani's absolute geometry and Lurie's spectral algebraic geometry

Alain Connes and Caterina Consani seem to be currently working on "absolute algebraic geometry", which is a kind of "algebraic geometry over the sphere spectrum" (https://arxiv.org/...
Peter Bonart's user avatar
54 votes
2 answers
4k views

Connections between various generalized algebraic geometries (Toen-Vaquié, Durov, Diers, Lurie)?

As far as I know, there are four possible ways to generalize algebraic geometry by 'simply' replacing the basic category of rings with something similar but more general: $\bullet$ In the approach by ...
Martin Brandenburg's user avatar