All Questions
9 questions
5
votes
0
answers
197
views
Bezout-type theorem for $p$-adic analytic plane curves
Let $p$ be a prime, and let $f,g \in \mathbb{Z}_p[[x,y]]$ be power series convergent on all of $\mathbb{Z}_p$. Suppose that the intersection of the analytic plane curves cut out by $f$ and $g$ is ...
3
votes
1
answer
180
views
Approximating $p$-adic power series by polynomials
Let $p$ be a prime, and let $f \in \mathbb{Z}_p[[x_1,\dots,x_d]]$ be a power series convergent on all of $\mathbb{Z}_p^d$. We make the following definition concerning the approximation of $f$ by ...
4
votes
1
answer
184
views
Meaning of dagger cohomology $H^{1 \dagger}(G^\dagger)$ in "Frobenius and Monodromy Operators" by Coleman and Iovita
Let $G$ be an abelian variety with good reduction over a finite extension $K$ of $\mathbb{Q}_p$. In equation (2.4) on page 179 of my edition of "The Frobenius and monodromy operators for curves ...
- 658
12
votes
1
answer
535
views
Open immersion of affinoid adic spaces
If $R$ and $S$ are complete Huber rings with $\varphi: R \to S$ a continuous map, then is it true in general that if $\mathrm{Spa}(S, S^\circ) \to \mathrm{Spa}(R, R^\circ)$ is an open immersion of ...
- 503
2
votes
1
answer
381
views
Reduced complete Tate ring which is not uniform?
Recall that a topological ring $A$ is Tate if there is an open subring $A_0$ such that the induced topology on $A_0$ is t-adic for some $t \in A_0$ that becomes a unit in $A.$ One can, given a Tate ...
- 217
9
votes
0
answers
327
views
What role, if any, do Archimedean valuations play in adic spaces?
I've been reading about adic spaces, and I couldn't help but wonder what would happen to the theory if one included in the definition of $Spa$ Archimedean valuations as well...?
Is there a weird ...
- 2,081
6
votes
0
answers
232
views
Complete characteristic p perfect Tate rings are uniform?
In Lemma 7.1.6 of his lecture notes on perfectoid spaces, Bhatt states that every complete characteristic p perfect Tate ring $A$ is uniform. In the proof he uses the Banach open mapping theorem on ...
- 61
4
votes
1
answer
1k
views
Iwasawa logarithm and analytic continuation
I am reading Number Theory vol. 1 by Henri Cohen (among other things) and I am curious about the Iwasawa logarithm. Let $\mathbb{C}_p$ be the completion of the algebraic closure of $\mathbb{Q}_p$.
...
- 539
8
votes
1
answer
726
views
What are the automorphisms of a perfectoid Tate algebra?
Let $K$ be a complete nonarchimedean field. The classical Tate algebra $K\langle T \rangle$ has lots of automorphisms, e.g., any substitution $T\mapsto a_1T+a_2T^2+\cdots$, where $a_1\in \mathcal{O}...
- 4,487