Timeline for What is the logical progression in algebraic tools for studying spaces (varieties -> schemes, sheaves, topos etc.)?
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| Aug 6, 2019 at 9:25 | comment | added | Andrej Bauer | I don't think it's a progression. You can make a progression from some views of space, but not all. For instance, "space as a datatype whose topology carries information-theoretic content" is not naturally reconcilable with notions of space arising in algebraic topology. | |
| Aug 6, 2019 at 8:00 | comment | added | i am circle | @jpp my elementary understanding is no doubt tripping us up here. As a physicist I'm used to using geometric and algebraic tools as methods for probing some aspects of spaces, say the shape of a magnetic field to interpret properties of particles, or shapes of fermionic fluids in topological insulators. I use the words "shape" and "space" as general property of physical systems. My question is: Since we are interested in describing more esoteric properties, how should I best think about the progression of these tools and the information they carry. Apologies if these questions are too vague | |
| Aug 6, 2019 at 7:05 | comment | added | user143954 | I am not sure one can think about a motive as a space. Motive remembers only the cohomological information, for some geometric questions that is not enough. That may be because I don't understand what exactly do you want (what do you mean by describing a space?). What is cohomology between objects? Do you mean higher direct image sheaves or something like relative homology from topology? | |
| Aug 6, 2019 at 6:45 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
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| Aug 6, 2019 at 6:45 | review | First posts | |||
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| Aug 6, 2019 at 6:42 | history | asked | i am circle | CC BY-SA 4.0 |