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LSpice
LSpice
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Representability of $Hom$\operatorname{Hom}(G_{\mathbb{Q}}, GL_2\operatorname{GL}_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$$F: \mathrm{Aff}/\textbf{Q}_p\longrightarrow \mathrm{Sets}$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$$\operatorname{Spec} A$ the set of representations $Hom(G_{\mathbb{Q}}, GL_2(A))$$\operatorname{Hom}(G_{\mathbb{Q}}, \operatorname{GL}_2(A))$.

Is this functor representable?

Representability of $Hom(G_{\mathbb{Q}}, GL_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$ the set of representations $Hom(G_{\mathbb{Q}}, GL_2(A))$.

Is this functor representable?

Representability of $\operatorname{Hom}(G_{\mathbb{Q}}, \operatorname{GL}_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: \mathrm{Aff}/\textbf{Q}_p\longrightarrow \mathrm{Sets}$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $\operatorname{Spec} A$ the set of representations $\operatorname{Hom}(G_{\mathbb{Q}}, \operatorname{GL}_2(A))$.

Is this functor representable?

edited body; edited title
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kindasorta
kindasorta
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Representability of $Hom(G_{\mathbb{Q}}, SL_2GL_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$ the set of representations $Hom(G_{\mathbb{Q}}, SL_2(A))$$Hom(G_{\mathbb{Q}}, GL_2(A))$.

Is this functor representable?

Representability of $Hom(G_{\mathbb{Q}}, SL_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$ the set of representations $Hom(G_{\mathbb{Q}}, SL_2(A))$.

Is this functor representable?

Representability of $Hom(G_{\mathbb{Q}}, GL_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$ the set of representations $Hom(G_{\mathbb{Q}}, GL_2(A))$.

Is this functor representable?

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kindasorta
kindasorta
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Representability of $Hom(G_{\mathbb{Q}}, SL_2)$

Let $G_{\mathbb{Q}}$ be the absolute Galois group of the rationals, and let $F: Aff/\textbf{Q}_p\longrightarrow Sets$ be the functor which associates to every affine $\mathbb{Q}_p$ scheme $Spec A$ the set of representations $Hom(G_{\mathbb{Q}}, SL_2(A))$.

Is this functor representable?