Timeline for A family of crystalline representations
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| Dec 7, 2018 at 23:53 | comment | added | Stanley Yao Xiao | @KevinBuzzard the most direct analogue in the higher dimensional case is if one sorts $S_F$ by the possible characteristic polynomials of Frobenius, which are necessarily Weil polynomials of degree $2g$. There are only finitely many of these (alternatively, the reductions mod $\mathbb{F}_v$ of the $A$'s determine these polynomials, and there are only finitely many abelian varieties defined over $\mathbb{F}_v$). I was hoping for a slightly more refined partition than this | |
| Dec 7, 2018 at 21:16 | comment | added | Kevin Buzzard | Why restrict to $K=\mathbb{Q}$ and $p\geq5$ in the $g=1$ case? Isn't this true in general when $g=1$? In general such a representation $\rho_A$ will have a crystalline Frobenius, and if you choose to partition $S_F$ up according to the slopes of this semilinear map then you will have an analogy of your decomposition in the $g=1$ case. | |
| Dec 7, 2018 at 17:38 | history | asked | Stanley Yao Xiao | CC BY-SA 4.0 |