Timeline for Semisimplicity of the p-adic étale Tate module over $F_p(t)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 12, 2021 at 17:51 | comment | added | Will Sawin | Given a subspace of the p-adic Tate module which, consider the quotient of the abelian variety by the $p^n$-torsion image of that subspace for all $n$. If these are isomorphic for infinitely many $n$ then I think you can check that the subspace is complemented. Then maybe you can bound the height and prove finiteness and deduce that infinitely many are isomorphic. | |
| Dec 12, 2021 at 17:47 | comment | added | Will Sawin | I tried to see if one could do something following either (1) Deligne's proof of semisimplicity of geometric monodromy for ell-adic etale cohomology or (2) the Arakelov-Faltings proof of the Tate conjecture for endomorphisms of abelian varieties over global fields. I don't think (1) works because the p-adic analogue would be in the setting of crystalline cohomology or something but the relationship between crystalline monodromy and monodromy of the p-adic Tate module is not obvious. But (2) might work. | |
| Jun 29, 2018 at 15:46 | comment | added | Emiliano Ambrosi | @TKe thank you for your answer. In that answer, k is a finite field, while here k is a finitely generated field. For the moment i'm not able to deduce the case when k is finitely generated from the situation when k is finite. | |
| Jun 29, 2018 at 10:46 | comment | added | user19475 | mathoverflow.net/questions/275355/… | |
| Jun 12, 2018 at 22:32 | history | asked | Emiliano Ambrosi | CC BY-SA 4.0 |