Timeline for Is there literature on a de Rham analogue of the Mumford-Tate group or ell-adic monodromy group?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2021 at 6:16 | comment | added | Julian Rosen | @YoYo My understanding of the Ogus conjecture is basically just Conjecture 7.1.7.3 from André's book. | |
| Apr 28, 2021 at 3:04 | comment | added | Angel65 | Hello @Julian Rosen, Can you help me for the problem appearing here : mathoverflow.net/questions/389391/… ; Thank you. :) | |
| May 6, 2019 at 21:04 | comment | added | Will Sawin | If the only thing you want is that it conjecturally agree with the motivic Galois group, you have many options - for instance you could take the Mumford-Tate or $\ell$-adic group, transfer it to de Rham cohomology by a period map, and take a $\mathbb Q$-Zariski closure. | |
| May 6, 2019 at 21:04 | comment | added | Will Sawin | In general, it's wrong to think of these groups as being associated to cohomology theories, but rather to the (Tannakian) categories these cohomology theories end up in - Galois representations, mixed Hodge structures, etc. So which structure you consider to be the de Rham Galois group depends on which category you want de Rham cohomology to lie in. | |
| May 6, 2019 at 20:59 | comment | added | Will Sawin | Your statement for the period conjecture is not the right one - it implies that the motivic Galois group of a disjoint union of $n$ points is $GL_n$. The right statement would be to take the smallest Zariski closed subset defined over $\mathbb Q$ containing the period matrix, translating it by any rational point of itself so it contains the identity, and then taking the subgroup it generates - this should be the motivic fundamental group of the Tannakian category of mixed Hodge structures. | |
| May 6, 2019 at 20:43 | history | asked | Julian Rosen | CC BY-SA 4.0 |