Strong approximation for a toric variety. (English) Zbl 1466.11043
In [U. Derenthal and D. Wei, J. Reine Angew. Math. 731, 235–258 (2017; Zbl 1396.11095)], a method to study strong approximation on algebraic varieties using descent theory is introduced. This method is then successfully applied to two classes of affine hypersurfaces.
In this paper, the author applies the same method to smooth toric varieties, proving the following result (Theorem 1.1).
Let \(k\) be a number field and \(v_0\) be a place of \(k\). Let \(X\) be a smooth toric variety over \(k\) with \(\overline{k}[X]^\times = \overline{k}^\times\). Let \(W\subset X\) be a closed subset of codimension at least \(2\). Then \(X\setminus W\) satisfies strong approximation with algebraic Brauer-Manin obstruction off \(v_0\).
In this paper, the author applies the same method to smooth toric varieties, proving the following result (Theorem 1.1).
Let \(k\) be a number field and \(v_0\) be a place of \(k\). Let \(X\) be a smooth toric variety over \(k\) with \(\overline{k}[X]^\times = \overline{k}^\times\). Let \(W\subset X\) be a closed subset of codimension at least \(2\). Then \(X\setminus W\) satisfies strong approximation with algebraic Brauer-Manin obstruction off \(v_0\).
Reviewer: Dino Festi (Mainz)
Citations:
Zbl 1396.11095References:
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