# Tagged Questions

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### Relative Leopoldt defect

Let F be a totally real number field such that the Leopoldt conjecture holds at a prime number $p$ and $M$ be a quadratic totally real extension of $F$. Is there a bound of the Leopoldt defect of $M$ ...
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### A $p$-adic sum of reciprocals of powers

Let $p$ be a prime number and $k\geq 2$ an even integer. Consider the following $p$-adic integer: $$S_{p,k} := \lim_{r\to+\infty} \sum_{a=1}^{p^r} \big(\frac{p^r}{a}\big)^k$$ Convergence is easy to ...
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### A multidimensional version of Hensel's lemma? (for more than one polynomial)

The classical Hensel's lemma is stated as follows: Let $f(x) \in \mathbb{Z}_p[x]$ and $a \in \mathbb{Z}_p$ satisfy $$|f(a)|_p < | f'(a) |_p^2.$$ Then there is a unique $\alpha \in \mathbb{Z}_p$...
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### a question about a result in Bushnell-Henniart book 'the local Langlands conjecture for GL(2)'

This might be a easy question, but I couldn't get the point. Let $F$ be a p-adic field, $\bar{F}$ a separable algebraic closure of $F$. Set $\Omega_F=Gal(\bar{F}/F)$. Use $F_{\infty}\subset \bar{F}$ ...
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### Torelli-like theorem for K3 surfaces on terms of its étale cohomology

Is there a proof of a Torelli-like Theorem for a K3-surface over any field (non complex) in terms of its etale or crystalline cohomology? For example: If $K\ne \mathbb{C}$ and \$X\rightarrow \...
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### If a unitsquare is partitioned into 101 triangles, is the area of one at least 1%?

Update: The answer to the title question is not necessarily, as pointed out by Tapio and Willie. I would be more interested in lower bounds. Monsky's famous and amazingly tricky proof says that if we ...
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### Reference for Ostrowski's 1916 Theorem?

I am looking for the original reference for Ostrowski's theorem of 1916 that the only valuations on the rational numbers are the trivial, Archimedean, and p-adic valuations. ...