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Arkandias
Arkandias
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Hello,

I am trying to compute a space of co-invariants.

$N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$'s on the diagonal

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien

Hello,

I am trying to compute a space of co-invariants.

$N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$'s on the diagonal

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien

Hello,

I am trying to compute a space of co-invariants.

$N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$'s on the diagonal

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks

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Arkandias
Arkandias
  • 991
  • 7
  • 15

N-coinvariants of the space of compactly$\mathcal{C}^{sm}_c(N,A)$ (compactly supported smooth functions on N$N$) ?

Hello,

I am trying to compute a space of co-invariants.   

$N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$s's on the diagonal.

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien

N-coinvariants of the space of compactly supported smooth functions on N ?

Hello,

I am trying to compute a space of co-invariants.  $N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$s on the diagonal.

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien

N-coinvariants of $\mathcal{C}^{sm}_c(N,A)$ (compactly supported smooth functions on $N$) ?

Hello,

I am trying to compute a space of co-invariants. 

$N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$'s on the diagonal

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien

Source Link
Arkandias
Arkandias
  • 991
  • 7
  • 15

N-coinvariants of the space of compactly supported smooth functions on N ?

Hello,

I am trying to compute a space of co-invariants. $N$ is the subgroup of $GL_2(Q_p)$ of upper triangular matrices with $1$s on the diagonal.

$E$ is a finite extension of $Q_p$, with ring of integers $\mathcal{O}_E$ and uniformizer $\varpi_E$, and $A$ is an artinian ring of the form : $\mathcal{O}_E / \varpi_E^n \mathcal{O}_E$.

I am considering the space $\mathcal{C}^{sm}_c(N,A)$ of compactly supported smooth functions on $N$, with the action of $N$ by right translation.

My problem is to show that $\mathcal{C}^{sm}_c(N,A)_N = 0$ (the space of coinvariants).

As I am not familiar with coinvariant computations I don't see how to show it. Any idea (or reference maybe) ?

Thanks, Julien