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comment splitting property of etale covering
For a counter-example to Q1, why not take $X = \mathrm{Spec}(\mathbb{Z}_p)$ and $Y \to X$ a totally ramified non-abelian Galois covering? Due to being totally ramified, the fibre over the closed point is just the the trivial extension of residue fields, hence clearly split.
Feb
3
comment Examples of NIP fields of characteristic $p$
This question might attract more interest if you included the definition of a NIP field.
Feb
3
comment First Galois cohomology of Weil restriction of $\mathbb{G}_m$
I agree with René that the result is a simple application of Shapiro's lemma. What else would you like?
Jan
31
awarded  Notable Question
Jan
26
comment Fiberwise criterion for a stack to be a gerbe
Just for fun: Example of a conic over $\mathbb{C}(s,t)$ with no rational point: $sx^2 + ty^2 = z^2$.
Jan
23
awarded  Popular Question
Jan
15
comment generic irreduciblity
mathoverflow.net/questions/57802/…
Jan
12
comment Elliptic curve over $\mathbb{Q}$ vs over $K$
Yes this follows from the fact that BSD is invariant under Weil restriction and isogeny. See my answer to this question: mathoverflow.net/questions/179764/a-question-on-bsd-conjecture/…. (This shows that BSD for E and its quadratic twist is equivalent to BSD for E_K)
Jan
12
answered A certain invariant of non-singular algebraic surfaces
Dec
28
awarded  Popular Question
Dec
24
awarded  Nice Answer
Dec
23
answered Conics, rational points and probability
Dec
18
answered Applications of the Galois embedding problem
Dec
9
awarded  Enlightened
Dec
9
awarded  Nice Answer
Dec
8
revised On cubic reciprocity for $x^3+y^3+z^3 = 996$?
deleted 1 character in body
Dec
8
answered On cubic reciprocity for $x^3+y^3+z^3 = 996$?
Nov
28
comment Arithmetically equivalent number fields and Langlands Program
The isomorphism from Prasad's paper comes from the fact that there is isomorphism of algebraic groups $\mathrm{R}_{F/\mathbb{Q}} \mathbb{G}_m \cong \mathrm{R}_{F'/\mathbb{Q}} \mathbb{G}_m$ over $\mathbb{Q}$ (here $\mathrm{R}_{F/\mathbb{Q}}$ denotes the Weil restriction). Perhaps you could obtain an isomorphism of the associated general linear groups is a similar way...?
Nov
28
comment Arithmetically equivalent number fields and Langlands Program
Perhaps you could edit your question to try to make it clearer?
Nov
28
comment Arithmetically equivalent number fields and Langlands Program
I agree with eric that the quantifiers in you question are not clear. Anyway, a theorem of Neukirch-Uchida states that any number field is determined by its absolute Galois group: en.wikipedia.org/wiki/Neukirch%E2%80%93Uchida_theorem. This suggests to me that all the automorphic data associated to a number field should determine it (though of course I can't make this more precise).