Timeline for formal group laws of Abelian varieties in positive characteristic
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jul 18, 2015 at 19:59 | history | suggested | Turbo |
tags added.
|
|
| Jul 18, 2015 at 19:38 | review | Suggested edits | |||
| S Jul 18, 2015 at 19:59 | |||||
| Feb 3, 2014 at 22:06 | comment | added | user76758 | It should be noted that identifying which $p$-divisible groups arise from abelian varieties is a rather subtle question (e.g., over finite fields of size $q$ there is a Weil-number restriction on the $q$-Frobenius, though there are further subtleties since a simple abelian variety may have non-isosimple $p$-divisible group), so it is quite remarkable that for many questions about abelian varieties in char. $p$ (such as for deformation theory) one can nonetheless reduce oneself to results that are valid more generally for $p$-divisible groups. | |
| Feb 3, 2014 at 16:52 | comment | added | abx | The theory of $p$-divisible groups associated to abelian varieties is very classical. You may want to start with Tate's lecture in the Driebergen conference on local fields (1966), or if you read french, with Serre's talk at the Bourbaki seminar, vol. 10 (1966-68). | |
| Feb 3, 2014 at 16:10 | comment | added | user76758 | For any (smooth, finite-dimensional) commutative formal group $G$ over a field of char. 0, the theory of logarithms provides an isomorphism to a power of the formal additive group. But in positive characteristic $p$ the formal group of an abelian variety "is" the identity component of its $p$-divisible group, so this has a rich theory of moduli in dimension $> 1$. In dimension 1 over a separably closed field, a $p$-divisible group with finite height is determined up to isomorphism by its height (e.g., height 1 for an ordinary elliptic curve, height 2 for a supersingular one). | |
| Feb 3, 2014 at 15:16 | history | edited | Dima Sustretov | CC BY-SA 3.0 |
deleted 1 characters in body
|
| Feb 3, 2014 at 15:11 | history | asked | Dima Sustretov | CC BY-SA 3.0 |