Dwork-type congruences and -adic ๐พ๐‘ connection

  • Alexander Varchenko

    University of North Carolina at Chapel Hill, USA
Dwork-type congruences and ๐‘-adic ๐พ๐‘  connection cover
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Abstract

We show that the -adic KZ connection associated with the family of curves has an invariant subbundle of rank , while the corresponding complex KZ connection has no nontrivial proper subbundles due to the irreducibility of its monodromy representation. The construction of the invariant subbundle is based on new Dwork-type congruences for associated Hasseโ€“Witt matrices.