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- W2346784247 abstract "To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the ℓ-adic counterpart of the GKZ hypergeometric system, which we call the ℓ-adic GKZ hypergeometric sheaf. It is an object in the derived category of ℓ-adic sheaves on the affine space over a finite field. Traces of Frobenius on stalks of this object at rational points of the affine space define the hypergeometric functions over the finite field introduced by Gelfand and Graev. We prove that the ℓ-adic GKZ hypergeometric sheaf is perverse, calculate its rank, and prove that it is irreducible under the non-resonance condition. We also study the weight filtration of the GKZ hypergeometric sheaf, determine its lisse locus, and apply our result to the study of weights of twisted exponential sums." @default.
- W2346784247 created "2016-06-24" @default.
- W2346784247 creator A5089969755 @default.
- W2346784247 date "2016-08-01" @default.
- W2346784247 modified "2023-10-18" @default.
- W2346784247 title "ℓ-adic GKZ hypergeometric sheaves and exponential sums" @default.
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- W2346784247 doi "https://doi.org/10.1016/j.aim.2016.04.021" @default.
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