Timeline for $\ell$-adic analogue of Kedlaya-Mochizuki
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| 4 hours ago | comment | added | Gabriel | Dear @R.vanDobbendeBruyn, the Riemann-Hilbert correspondence gives an equivalence of categories between regular holonomic D-modules on a complex algebraic variety and perverse sheaves on its analytification. What I mean is truly different. For example, let X be a finite type scheme over the integers then base change it to a scheme X_0 over C and X_p over F_p. I mean that holonomic D-modules on X_0 "behave similarly" to l-adic perverse sheaves on X_p. Contrarily to RH, this is not a theorem. Only a large collection of analogies. | |
| 7 hours ago | answer | added | Will Sawin | timeline score: 6 | |
| 7 hours ago | comment | added | Function | Hi Remy: In positive char, irregular singularities morally correspond to wild ramifications. For example, on A1, Artin-Schreier serves as an analogue of (O, d + dt). | |
| 7 hours ago | comment | added | R. van Dobben de Bruyn | Some online searching gives papers explaining exactly that: to even state an irregular Riemann–Hilbert correspondence, one first needs to find an appropriate enlargement of constructible sheaves that is engineered to upgrade the correspondence. So I don't think this translates to naturally arising questions on perverse sheaves. | |
| 7 hours ago | comment | added | R. van Dobben de Bruyn | I'm not an expert on the de Rham side (D-modules), but isn't the analogy between perverse sheaves and regular holonomic D-modules? So from that point of view, the irregular ones would sort of look like "junk", at least in the sense that they have no $\ell$-adic (or Betti) analogue. | |
| 7 hours ago | history | asked | Gabriel | CC BY-SA 4.0 |