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Uniformizer for splitting field of p^{1/p^n} over padics
I am pretty sure that the answer is "no, it's too messy". If however somebody does have an answer, then we could use it to study the field of norms of the union of all those fields, and I'd be very interested in that. 
Feb
7 
comment 
When does the radius of convergence of the product of two $p$adic power series increase?
Have you looked at "Rank one solvable padic differential equations and finite Abelian characters via Lubin–Tate groups" by Andrea Pulita? The abstract starts with "We introduce a new class of exponentials of Artin–Hasse type, called πexponentials". 
Feb
2 
answered  Examples of padic representations 
Jan
27 
comment 
HodgeTate representations
A simpler example would be a nontrivial extension of $Q_p$ by $Q_p(1)$. 
Apr
30 
awarded  Yearling 
Apr
20 
revised 
HodgeTate weights of induced representation
added 154 characters in body 
Apr
20 
answered  HodgeTate weights of induced representation 
Apr
8 
awarded  Popular Question 
Apr
8 
comment 
Algebraic integer with conjugates on the unit circle
The same is true of $\alpha^k$ and the characteristic polynomials of the $\alpha^k$ have coeffts that are bounded indept of $k$. A lot of them must be equal to each other, so $\alpha^k = \alpha^\ell$ for some $k$ and $\ell$. 
Apr
8 
answered  examples of nonunique factorisation in cyclotomic fields 
Mar
1 
comment 
Can an abelian variety/Q have no nontrivial points over Q_sol?
@Pablo sorry, my mistake! 
Mar
1 
comment 
Can an abelian variety/Q have no nontrivial points over Q_sol?
By definition, an abelian variety over a field K has a rational point over K, so in your question, you presumably mean a homogenous space for your abelian variety. 
Jan
27 
comment 
Number of common solutions of polynomial system
See for instance the introduction to arxiv.org/abs/1408.3224 
Jan
27 
answered  integral padic Hodge theory and de Rham representations 
Sep
5 
revised 
Openness of finite index subgroups of $\mathrm{GL}_n(\prod O_v)$
added 59 characters in body 
Sep
5 
answered  Openness of finite index subgroups of $\mathrm{GL}_n(\prod O_v)$ 
Aug
26 
awarded  Enlightened 
Aug
6 
awarded  Custodian 
Aug
6 
reviewed  Reject nontrivial theorems with trivial proofs 
Jul
26 
comment 
Linear map with two “incompatible” representations
Very nice, thank you! 