Iterated integrals on the Legendre family of elliptic curves
Eisuke Otsuka

TL;DR
This paper extends Chen's comparison isomorphism for iterated integrals to the Legendre family of elliptic curves, advancing algebraic-geometric methods for understanding periods.
Contribution
It develops an analogue of Chen's comparison isomorphism specifically for iterated integrals on the Legendre family of elliptic curves.
Findings
Establishes a new comparison isomorphism for elliptic curve periods
Bridges algebraic geometry and iterated integrals in elliptic settings
Provides tools for studying periods via iterated integrals on elliptic curves
Abstract
K.T. Chen showed that iterated integrals give comparison isomorphisms between the cohomologies of bar complexes and fundamental group rings. This led to the development of an algebraic-geometric approach to studying periods given by iterated integrals. In this paper we consider an analogue of this comparison isomorphism theorem for iterated integrals on the Legendre family.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology
