Dwork-type congruences and $p$-adic KZ connection

Alexander Varchenko

Dwork-type congruences and $p$-adic KZ connection

Number Theory 2022-05-04 v1 Mathematical Physics Algebraic Geometry Classical Analysis and ODEs math.MP

Authors: Alexander Varchenko

Abstract

We show that the $p$ -adic KZ connection associated with the family of curves $y^q=(t-z_1)\dots (t-z_{qg+1})$ has an invariant subbundle of rank $g$ , 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 Hasse--Witt matrices.

Keywords

principal bundles p-adic hodge theory vector bundles

Cite

@article{arxiv.2205.01479,
  title  = {Dwork-type congruences and $p$-adic KZ connection},
  author = {Alexander Varchenko},
  journal= {arXiv preprint arXiv:2205.01479},
  year   = {2022}
}

Comments

Latex, 26 pages. arXiv admin note: substantial text overlap with arXiv:2108.12679

Dwork-type congruences and $p$-adic KZ connection

Abstract

Keywords

Cite

Comments

Related papers