Corpus ID: 236635404

The Universal Elliptic KZB Connection in Higher Level

@inproceedings{Hopper2021TheUE,
  title={The Universal Elliptic KZB Connection in Higher Level},
  author={E. Hopper},
  year={2021}
}
The level N elliptic KZB connection is a flat connection over the universal elliptic curve in level N with its N-torsion sections removed. Its fiber over the point (E, x) is the unipotent completion of π1(E − E[N ], x). It was constructed by Calaque and Gonzalez. In this paper, we show that the connection underlies an admissible variation of mixed Hodge structure and that it degenerates to the cyclotomic KZ connection over the singular fibers of the compactified universal elliptic curve. 

References

SHOWING 1-10 OF 31 REFERENCES
Racinet: Towards multiple elliptic polylogarithms, unpublished preprint, 2007, [arXiv:math/0703237
  • KZB CONNECTION IN HIGHER LEVEL
  • 2007
On the universal ellipsitomic KZB connection
We construct a twisted version of the genus one universal Knizhnik-Zamolodchikov-Bernard (KZB) connection introduced by Calaque-Enriquez-Etingof, that we call the ellipsitomic KZB connection. This isExpand
Contributions to the theory of KZB associators
In this thesis, following the work initiated by V. Drinfeld and pursued by B. Enriquez, then by the latter together with D. Calaque and P. Etingof, we study the universal twisted ellipticExpand
P
  • Etingof: Universal KZB equations: the elliptic case, in Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, Progr. Math., 269, Birkhäuser, Boston
  • 2009
Cyclotomic and Elliptic Polylogarithms and Motivic Extensions of Q by Q(m)
  • Ph.D. thesis, Duke University,
  • 2021
The elliptic KZB connection and algebraic de Rham theory for unipotent fundamental groups of elliptic curves
In this paper, we develop an algebraic de Rham theory for unipotent fundamental groups of once punctured elliptic curves over a field of characteristic zero using the universal elliptic KZBExpand
Rational homotopy theory
1 The Sullivan model 1.1 Rational homotopy theory of spaces We will restrict our attention to simply-connected spaces. Much of this goes through with nilpotent spaces, but this will keep thingsExpand
Relations between Derivations arising from Modular Forms
Denote by L(a, b) the free complex Lie algebra on the two generators a and b. For each integer m ≥ 0 there is a derivation 2m on L(a, b) that satisfies 2m([a, b]) = 0 and 2m(a) = ad(a) (b). In thisExpand
...
1
2
3
4
...