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MTS
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how How to computercompute the first derived direct image along an open immersion, for the fppf sheaf represented by a multiplicative group?

Let $S=Spec R$$S=\mathrm{Spec}(R)$, $s=Spec\: k$$s=\mathrm{Spec}(k)$ and $\eta=Spec\:K$$\eta=\mathrm{Spec}(K)$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to computercompute the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.

how to computer the first derived direct image along an open immersion, for the fppf sheaf represented by a multiplicative group?

Let $S=Spec R$, $s=Spec\: k$ and $\eta=Spec\:K$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to computer the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.

How to compute the first derived direct image along an open immersion, for the fppf sheaf represented by a multiplicative group?

Let $S=\mathrm{Spec}(R)$, $s=\mathrm{Spec}(k)$ and $\eta=\mathrm{Spec}(K)$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to compute the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.

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Heer
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how to computer the first derived direct image along an open immersion, for the fppf sheaf represented by a multiplicative group?

Let $S=Spec R$, $s=Spec\: k$ and $\eta=Spec\:K$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to computer the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.