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Arithmetic intersection on GSpin Rapoport-Zink spaces

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arxiv 1702.07848 v1 pith:33G4ROCK submitted 2017-02-25 math.NT math.AG

classification math.NTmath.AG
keywords arithmeticcaseformulagspinintersectionminusculeorthogonalrapoport-zink
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We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport-Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan-Gross-Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic-geometric side of the arithmetic fundamental lemma proved by Rapoport-Terstiege-Zhang in the minuscule case.

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