Leiden University Student Repository

Kalker, Felix (2025)

The Knopp cocycle and cycle integrals of the j-function

Master thesis | Mathematics (MSc)

The j-invariant of an elliptic curve with complex multiplication generates the ring class field of the respective order over its fraction field. Gross and Zagier’s work gives an explicit factorisation for the differences of such j-invariants, which has led to much of the knowledge we have today on the BSD conjecture. Recently, Darmon and Vonk defined an analagous p-adic ‘RM-theory’, which (conjecturally) behaves in all key respects like the differences of CM singular moduli. We will give a connection between this p-adic RM-theory and geodesic integrals of the j-function, and investigate the possibility of a complex analytic RM-theory.

RM-Theory

j-function

modular geodesics

linking numbers

Knopp cocycle

Author

Kalker, Felix

Faculty

Faculty of Science

Specialisation

Algebra, Geometry and Number Theory

Supervisors

Vonk, J.B.

ECTS Credits

40

Language

en