Abstract:This note concerns exponential sheaves, their realizations, and Fourier transforms. We construct realization functors from relative categories of exponential sheaves to holonomic (not necessarily regular) D-modules and show that they are t-exact and faithful on the heart. We develop a "universal" Fourier transform on these categories that commutes with classical Fourier transforms under realizations. The categories considered also admit weight structures that satisfy the usual formalism. The "universal" Fourier transform is shown to preserve purity. The motivation is N. Katz's 'analogies' between exponential sums over finite fields and differential equations.
From: Rahbar Virk [view email]
[v1]
Thu, 14 May 2026 14:40:40 UTC (9 KB)
[v2]
Mon, 18 May 2026 13:47:38 UTC (12 KB)
[v3]
Fri, 29 May 2026 14:34:15 UTC (17 KB)
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