The purity locus of matrix Kloosterman sums

Erdélyi, Márton Kristóf and Sawin, Will and Tóth, Árpád (2024) The purity locus of matrix Kloosterman sums. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 377 (6). pp. 4117-4132. ISSN 0002-9947

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Abstract

We construct a perverse sheaf related to the the matrix exponential sums investigated by Erdélyi and Tóth [ Matrix Kloosterman sums , 2021, arXiv:2109.00762]. As this sheaf appears as a summand of certain tensor product of Kloosterman sheaves, we can establish the exact structure of the cohomology attached to the sums by relating it to the Springer correspondence and using the recursion formula of Erdélyi and Tóth.

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