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Chris Wuthrich
Chris Wuthrich
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Is $H^{1}_{Sel}\left(K,E_{p^{n}}\right)\rightarrow\prod_{q \text{ a nonarchimedean prime of }K\nmid \infty}\left H^1\left(K_{q},E_{p^{n}}\right)$ an injection?

If $K$ is a number field, $E$ an elliptic curve and $p$ a prime, does the Selmer group $$H^{1}_{\operatorname{Sel}}\left(K,E_{p^{n}}\right)$$ always inject into $$\prod_{q \text{ a nonarchimedean prime of }K}\left(K_{q},E_{p^{n}}\right)$$$$\prod_{q \text{ a nonarchimedean prime of }K}H^1 \left(K_{q},E_{p^{n}}\right)$$ (Excuse me if that question is stupid)

Is $H^{1}_{Sel}\left(K,E_{p^{n}}\right)\rightarrow\prod_{q \text{ a nonarchimedean prime of }K}\left(K_{q},E_{p^{n}}\right)$ an injection?

If $K$ is a number field, $E$ an elliptic curve and $p$ a prime, does the Selmer group $$H^{1}_{\operatorname{Sel}}\left(K,E_{p^{n}}\right)$$ always inject into $$\prod_{q \text{ a nonarchimedean prime of }K}\left(K_{q},E_{p^{n}}\right)$$ (Excuse me if that question is stupid)

Is $H^{1}_{Sel}\left(K,E_{p^{n}}\right)\rightarrow\prod_{q \nmid \infty} H^1\left(K_{q},E_{p^{n}}\right)$ an injection?

If $K$ is a number field, $E$ an elliptic curve and $p$ a prime, does the Selmer group $$H^{1}_{\operatorname{Sel}}\left(K,E_{p^{n}}\right)$$ always inject into $$\prod_{q \text{ a nonarchimedean prime of }K}H^1 \left(K_{q},E_{p^{n}}\right)$$ (Excuse me if that question is stupid)

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The Thin Whistler
The Thin Whistler
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Is $H^{1}_{Sel}\left(K,E_{p^{n}}\right)\rightarrow\prod_{q \text{ a nonarchimedean prime of }K}\left(K_{q},E_{p^{n}}\right)$ an injection?

If $K$ is a number field, $E$ an elliptic curve and $p$ a prime, does the Selmer group $$H^{1}_{\operatorname{Sel}}\left(K,E_{p^{n}}\right)$$ always inject into $$\prod_{q \text{ a nonarchimedean prime of }K}\left(K_{q},E_{p^{n}}\right)$$ (Excuse me if that question is stupid)