MathOverflow

$G(k)$, as usual, is the smallest number such that every large integer is the sum of $k$th non negative powers. Let $G_r(k)$ be the restricted Waring's number, where we add the requirement that all the $k$th powers are distinct. What can be said about...

In Kedlayas lecture notes on $\delta$-rings he claims that for $A=\mathbb{Z}[\mu_n : gcd(n,p)=1]$ together with the automorphism $\phi : A\to A, \zeta _n\mapsto \zeta_n ^p$, the $\delta$-constants (meaning $\delta(x) = \frac{\phi(x)-x^p}{p}=0$) are given...

In principle, a mathematical paper should be complete and correct. New statements should be supported by appropriate proofs. But this is only theory. Because we often cannot enter into the smallest details, we "prove" wrong statements here and then....

Let $K$ be a field with discrete valuation $v$ and residue field $k$ of char $p$, $A$ an abelian variety over $K$. Denote $K^s$ a separable closure of $K$ with valuation $\overline{v}$ extending $v$ and $I \subset \operatorname{Gal}(K^s/K)$ the inertia...