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YCor
YCor
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Are Do complex varieties have a dense open subset with residually finite on some openfundamental group?

Let $S$ be a smooth connected variety over the complex numbers. The fundamental group might not be residually finite (i.e., the morphismhomomorphism $pi_1(S(\mathbb C)) \to pi_1^{et}(S)$$\pi_1(S(\mathbb C)) \to \pi_1^{\mathrm{et}}(S)$ might not be injective).

Is there a dense Zariski open subset $U\subset S$ such that $\pi_1(U(\mathbb C)) $ is residually finite?

Are varieties residually finite on some open

Let $S$ be a smooth connected variety over the complex numbers. The fundamental group might not be residually finite (i.e., the morphism $pi_1(S(\mathbb C)) \to pi_1^{et}(S)$ might not be injective).

Is there a dense open $U\subset S$ such that $\pi_1(U(\mathbb C)) $ is residually finite?

Do complex varieties have a dense open subset with residually finite fundamental group?

Let $S$ be a smooth connected variety over the complex numbers. The fundamental group might not be residually finite (i.e., the homomorphism $\pi_1(S(\mathbb C)) \to \pi_1^{\mathrm{et}}(S)$ might not be injective).

Is there a dense Zariski open subset $U\subset S$ such that $\pi_1(U(\mathbb C)) $ is residually finite?

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Randy
Randy
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Are varieties residually finite on some open

Let $S$ be a smooth connected variety over the complex numbers. The fundamental group might not be residually finite (i.e., the morphism $pi_1(S(\mathbb C)) \to pi_1^{et}(S)$ might not be injective).

Is there a dense open $U\subset S$ such that $\pi_1(U(\mathbb C)) $ is residually finite?