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arXiv · 2505.04039

Dwork congruences via q-deformation

Pavan Kartik·Andrey Smirnov
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Abstract

We consider a system of polynomials $T_{s}(z,q)\in\mathbb{Z}[z,q]$ which appear as truncations of the K-theoretic vertex function for the cotangent bundles over Grassmannians $T^{*}Gr(k,n)$. We prove that these polynomials satisfy a natural $q-$deformation of Dwork's congruences \[\frac{T_{s+1}(z,q)}{T_{s}(z^{p},q^{p})}\equiv\frac{T_{s}(z,q)}{T_{s-1}(z^{p},q^{p})}\text{ (mod } [p^{s}]_{q})\] In the limit $q\to 1$ we recover the main result of arXiv:2302.03092v3

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Pavan Kartik, Andrey Smirnov. 2025-05-07. Dwork congruences via q-deformation. https://arxiv.org/abs/2505.04039

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