Strong approximation for a toric variety

Dasheng Wei

Strong approximation for a toric variety

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arxiv 1403.1035 v3 pith:OHL2GE6U submitted 2014-03-05 math.NT math.AG

Dasheng Wei This is my paper · ORCID

classification math.NTmath.AG

keywords approximationkbarstrongsubsettimestoricvarietyalgebraic

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Let X be a toric variety over a number field k with \kbar[X]^\times=\kbar^\times. Let W\subset X be a closed subset of codimension at least 2. We prove that X\setminus W satisfies strong approximation with algebraic Brauer--Manin obstruction.

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Brauer-Manin obstruction for Erd\H{o}s-Straus surfaces
math.NT 2019-08 accept novelty 7.0 of 10

For every n, the Brauer-Manin obstruction does not obstruct positive integer solutions to the Erdos-Straus equation, yet it gives a universal local condition (a product of Hilbert symbols equal to -1) for all such solutions.

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