July 1, 2022 Q: Is the property formal of an algebraic variety invariant under base extension? Let $X$ be a scheme of finite type over a base field $k$, and $A$ an $A_k$ algebra. Let $V$ be a quasi-finite, separated scheme over $k$ which has a finite number of generic points. Is it true that $X\times_k V$ is separated and of finite type over $V$, and that $X\times_k V$ is the formal completion of $X$ along $V$? The question is the same but with algebraic spaces instead of varieties. My hope is that there is a reference for this, but alas I did not find it. A: Yes. This is easily seen using Zariski’s Main Theorem (or equivalently the Nagata compactification). If $K$ is a field, a ring $A$ is Noetherian iff it is quasi-finite over $K$ and Cohen-Macauly over $K$. Now let $K$ be an algebraic closure of $k$. By the Main Theorem, $A$ is Noetherian over $K$ iff it is quasi-finite over $k$ and Cohen-Macaulay over $k$. The result you want follows from this. To see that $X\times_k V$ is separated and of finite type over $V$, first note that since $X\times_k V$ is separated, $V$ is separated. Since $V$ is finite over $k$, it has only finitely many points. Thus, the only problem is to show that $X\times_k V$ has only finitely many closed points. But this follows from the fact that $X$ has only finitely many closed points. As for the completion along a subset $U\subseteq X$, it is the object of the following “local argument”. Let $U$ be a subset of $X$, let $O=\mathrm{Spec}(A)$ be the affine scheme underlying $X$, and let $\mathcal{O}=\mathcal{O}_A$ be the structure sheaf of $O$. We can identify the category of affine schemes (resp. affine

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Q: Date comparison based on month – SQL Server I have two dates in SQL Server @startDate DATE = 2/3/2016 @endDate DATE = 3/3/2016 How can I find, for example, the following items: Row of data that is between @startDate and @endDate, where the month is between Jan and Mar. Row of data that is between @startDate and @endDate, where the month is between Jan and Feb and between March and April. Row of data that is between @startDate and @endDate, where the month is between Feb and March. Thanks A: something like this: SET @startDate = DATEADD(MONTH,DATEDIFF(MONTH,0,@startDate),0); SET @endDate = DATEADD(MONTH,1,@endDate) ;WITH dates AS ( SELECT @startDate as d1 UNION ALL SELECT DATEADD(MONTH,1,d1) FROM dates d1 INNER JOIN dates d2 ON d1.d2 Carbon fiber producing methods of the related art include a method of producing a carbon fiber by carbonizing a polyacrylonitrile type polymer fiber having a weight average fiber diameter of 0.5 μm or less and/or a so-called salt pyrolysis method of producing a carbon fiber by a salt pyrolysis process of polyacrylonitrile type polymer fiber having a weight average fiber diameter of 0.5 μm or less, and subsequently subjecting the resultant carbon fiber to a heat treatment for carbonizing the carbon fiber to obtain a carbon fiber (for example, refer to

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