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comment Uniformizer for splitting field of p^{1/p^n} over p-adics
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 p-adic 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 π-exponentials".
Feb
2
answered Examples of p-adic representations
Jan
27
comment Hodge-Tate representations
A simpler example would be a non-trivial extension of $Q_p$ by $Q_p(-1)$.
Apr
30
awarded  Yearling
Apr
20
revised Hodge-Tate weights of induced representation
added 154 characters in body
Apr
20
answered Hodge-Tate 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 non-unique factorisation in cyclotomic fields
Mar
1
comment Can an abelian variety/Q have no non-trivial points over Q_sol?
@Pablo sorry, my mistake!
Mar
1
comment Can an abelian variety/Q have no non-trivial 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 p-adic 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!