# ag.algebraic geometry – Is the unipotent part map of hyperbolic spherical over native bailiwick injective? retort

Hello pricey customer to our community We will proffer you an answer to this query ag.algebraic geometry – Is the unipotent part map of hyperbolic spherical over native bailiwick injective? ,and the retort will breathe typical via documented info sources, We welcome you and proffer you contemporary questions and solutions, Many customer are questioning concerning the retort to this query.

## ag.algebraic geometry – Is the unipotent part map of hyperbolic spherical over native bailiwick injective?

Let $$X/mathbb{Z}_p$$ breathe a light-weight hyperbolic spherical and $$pi^{un}_1(X_{overline{mathbb{Q}_p}},b)$$ denotes the pro-unipotent completion(over $$mathbb{Q}_p$$) of the etale basic group of $$X$$ foundation modified to $$overline{mathbb{Q}_p}$$ based mostly at some extent $$bin X(mathbb{Z}_p)$$. Then we maintain a map from $$X(mathbb{Z}_p)$$ to $$H^1(Gal(overline{mathbb{Q}_p}/mathbb{Q}_p),pi^{un}_1(X_{overline{mathbb{Q}_p}},b))$$ by sending $$xin X(mathbb{Z}_p)$$ to the (cohomology class of) path torsor $$P(b,x)$$.

My questions is: is that this map all the time injective?

we are going to proffer you the answer to ag.algebraic geometry – Is the unipotent part map of hyperbolic spherical over native bailiwick injective? query by way of our community which brings all of the solutions from a number of reliable sources.