| Full text | |
| Author(s): |
Fonseca, Tiago J.
;
Matthes, Nils
Total Authors: 2
|
| Document type: | Journal article |
| Source: | ALGEBRA & NUMBER THEORY; v. 19, n. 7, p. 60-pg., 2025-01-01. |
| Abstract | |
Using the formalism of bar complexes and their relative versions, we give a new, purely algebraic, construction of the so-called universal elliptic KZB connection in arbitrary level. We compute explicit analytic formulae, and we compare our results with previous approaches to elliptic KZB equations and multiple elliptic polylogarithms in the literature. Our approach is based on a number of results concerning logarithmic differential forms on universal vector extensions of elliptic curves. Let S be a scheme of characteristic 0, E -> S be an elliptic curve, f: E# -> S be its universal vector extension, and pi : E# -> E be the natural projection. Given a finite subset of torsion sections Z subset of E(S), we study the dg-algebra over OS of relative logarithmic differentials A = f*center dot center dot E#/S(log pi-1Z). In particular, we prove that the residue exact sequence in degree 1 splits canonically, and we derive the formality of A. When S is smooth over a field k of characteristic 0, we also prove that sections of A1 admit canonical lifts to absolute logarithmic differentials in f*center dot 1E#/k(log pi-1 Z), which extends a well-known property for regular differentials given by the "crystalline nature" of universal vector extensions. (AU) | |
| FAPESP's process: | 20/15804-1 - Periods and algebraicity |
| Grantee: | Tiago Jardim da Fonseca |
| Support Opportunities: | Research Grants - Young Investigators Grants |