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Hypergeometric Integrals Modulo $p$ and Hasse--Witt Matrices

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 نشر من قبل Svetlana Varchenko
 تاريخ النشر 2020
  مجال البحث فيزياء
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We consider the KZ differential equations over $mathbb C$ in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $mathbb F_p$. We study the space of polynomial solutions of these differential equations over $mathbb F_p$, constructed in a previous work by V. Schechtman and the second author. Using Hasse-Witt matrices we identify the space of these polynomial solutions over $mathbb F_p$ with the space dual to a certain subspace of regular differentials on an associated curve. We also relate these polynomial solutions over $mathbb F_p$ and the hypergeometric solutions over $mathbb C$.



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