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2 votes
1 answer
178 views

Can we get a homomorphism between two elliptic curves if we know a homomorphism between the ...

Let $E_1$ and $E_2$ be two elliptic curves over a field of characteristic $0$, and let $\hat{E_1}$ and $\hat{E_2}$ be two formal group laws associated with $E_1$ and $E_2$, respectively. It is known t …
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  • 195
5 votes
0 answers
235 views

Does a simple formal group give rise to a simple Lie algebra?

A formal group $F$ is an intermediate object between Lie group $G$ and Lie algebra $\mathfrak{g}$. A formal group is called simple if it has no nontrivial sub-formal group. On the other hand, a simple …
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  • 195
1 vote
0 answers
122 views

Does the torsion points of abelian varieties transfer to their formal group laws (upon suita...

Let $A$ and $B$ be two abelian varieties over any algebraically closed field. Let $A[p^n]$ and $B[p^n]$ denotes the set of $p$-power torsion points of $A$ and $B$. Assume that $A[p^n]$ and $B[p^n]$ h …
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  • 195
1 vote
0 answers
214 views

What is the relation between two abelian varieties that have the same formal group?

Consider two abelian varieties $A$ and $B$ over the $p$-adic number field $\mathbb{Q}_p$. Let $\hat{A}$ and $\hat{B}$ be the associated formal groups of $A$ and $B$, respectively. Assume that $\hat{A} …
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  • 195
0 votes
0 answers
102 views

looking for reference for two elliptic curves with equal formal group

I am looking for a reference. In this post, @Chris Wurthrich made the following comment: If the formal group laws (probably upon particular choice of coordinates) of two elliptic curves over any ring …
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  • 195
5 votes
0 answers
148 views

When is the image of $\operatorname{Gal}(\bar K/K)$ open in $\operatorname{Aut}(V)$, where $...

Let $K$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $A$. Let $F$ be a $p$-divisible group and $T$ be the Tate module. Consider the vector space $V=T \otimes_{\mathbb{Q}_p} C$, where …
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  • 195