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edit approved Jan 22, 2015 at 18:38
jmc
edit approved Jan 22, 2015 at 18:38
jmc
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Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$$\rho: G\to \mathrm{GL}(V\otimes_k K)$.

Thanks!

Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$.

Thanks!

Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to \mathrm{GL}(V\otimes_k K)$.

Thanks!

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Mostafa - Free Palestine
Mostafa - Free Palestine
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Tannakian fundamental group forof two explicit tensor categories

Let $K/k$ is a field extension and $G$ is an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$.

Thanks!

Tannakian fundamental group for two explicit tensor categories

Let $K/k$ is a field extension and $G$ is an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$.

Thanks!

Tannakian fundamental group of two explicit tensor categories

Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$.

Thanks!

Source Link
Mostafa - Free Palestine
Mostafa - Free Palestine
  • 4.5k
  • 1
  • 18
  • 44

Tannakian fundamental group for two explicit tensor categories

Let $K/k$ is a field extension and $G$ is an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):

1. The category of pairs of finite vector spaces over $k$ with an isomorphism of their extensions to $K$,

2. The category of finite vector spaces $V$ over $k$ with a representation $\rho: G\to V\otimes_k K$.

Thanks!