Timeline for Super mixed Hodge structures?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2021 at 13:48 | comment | added | Ben Webster♦ | @AntonMellit Maybe you had this in mind already, but the ODE story is quite precisely true if you take the corresponding twistor: you take $z^sV[z,z^{-1}]$ as a bundle with flat connection on $\mathbb{C}^*$, and then the two Hodge filtrations tell you how to extend over $0$ and $\infty$. I think you should exactly get what you said about growth rates of flat sections recovering the Hodge filtrations (by construction). Being an honest Hodge structure means you get actual flat sections, rather than multi-valued ones. | |
| Dec 13, 2021 at 13:13 | comment | added | Anton Mellit | From some points of view (gamma motives and hypergeometric motives) it makes sense to extend even further: to allow Hodge structures to have a "phase" in $[0,1)$, so that usual Hodge structures have phase $0$, your odd Hodge structures have phase $1/2$, but for general phase $s$ the Hodge filtratiion is indexed by elements of $\mathbb{Z}+s$. It's like take some differential equation. Then the space of solutions around the origin is filtered by their growth: if a solution starts with $t^s$ you put it in $F_s$. | |
| Dec 13, 2021 at 9:51 | history | became hot network question | |||
| Dec 13, 2021 at 9:22 | answer | added | Balazs | timeline score: 6 | |
| Dec 13, 2021 at 9:18 | history | edited | YCor | CC BY-SA 4.0 |
removed capital in title, added top-level tag
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| Dec 13, 2021 at 7:26 | answer | added | Dmitry Vaintrob | timeline score: 4 | |
| Dec 13, 2021 at 2:02 | history | edited | LSpice | CC BY-SA 4.0 |
Title of BGS; DOI link
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| Dec 13, 2021 at 1:49 | history | asked | Ben Webster♦ | CC BY-SA 4.0 |