Compute all homomorphisms of $mathbb G_a$ to $SL_2$ over $mathbb Z$
4
$begingroup$
How to compute the set of homomorphisms $mathrm{Hom}left(mathbb G_a , SL_2right)$ between those two group schemes over $mathbb Z$?
Over $mathbb C$, this can be done using classical algebraic geometry, up to $SL_2$ conjugacy.
group-theory algebraic-groups group-homomorphism
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
$endgroup$
add a comment |
4
$begingroup$
How to compute the set of homomorphisms $mathrm{Hom}left(mathbb G_a , SL_2right)$ between those two group schemes over $mathbb Z$?
Over $mathbb C$, this can be done using classical algebraic geometry, up to $SL_2$ conjugacy.
group-theory algebraic-groups group-homomorphism
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
$endgroup$
$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02
add a comment |
4
4
4
2
$begingroup$
How to compute the set of homomorphisms $mathrm{Hom}left(mathbb G_a , SL_2right)$ between those two group schemes over $mathbb Z$?
Over $mathbb C$, this can be done using classical algebraic geometry, up to $SL_2$ conjugacy.
group-theory algebraic-groups group-homomorphism
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
$endgroup$
How to compute the set of homomorphisms $mathrm{Hom}left(mathbb G_a , SL_2right)$ between those two group schemes over $mathbb Z$?
Over $mathbb C$, this can be done using classical algebraic geometry, up to $SL_2$ conjugacy.
group-theory algebraic-groups group-homomorphism
group-theory algebraic-groups group-homomorphism
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
edited Dec 21 '18 at 10:58
Johannes Huisman
3,135617
3,135617
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
asked Dec 21 '18 at 3:25
zzyzzy
2,6111420
2,6111420
$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02
add a comment |
$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02
$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02
add a comment |
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$begingroup$
You can try working $bmod p$ for all primes $p$.
$endgroup$
– Qiaochu Yuan
Dec 21 '18 at 7:22
$begingroup$
What do you mean by "compute the set"? you seem to implicitly mean that you want up to conjugacy in some sense, which is the main difficulty.
$endgroup$
– YCor
Dec 21 '18 at 15:02