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The zeta-function of a $p$-adic manifold, Dwork theory for physicists

2007
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Communications in Number Theory and Physics
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In this article we review the observation, due originally to Dwork, that the ζ-function of a variety, defined originally over the field with p elements, is a superdeterminant. We review this observation in the context of the family of quintic 3-folds, x i = 0, and study the ζ-function as a function of the parameter ϕ. Owing to cancellations, the superdeterminant of an infinite matrix reduces to the (ordinary) determinant of a finite matrix, U (ϕ), corresponding to the action of the Frobenius

doi:10.4310/cntp.2007.v1.n3.a2
fatcat:dpk3vjuxqnegfas23delwdv47i