Precise determination of pion-nucleon scattering amplitudes and the nucleon sigma-term

In this talk we will review how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy-Steiner equations, allows for a precise determination of pion-nucleon scattering at low energies.
Then, we will discuss the extraction of the nucleon sigma-term via the Cheng–Dashen low-energy theorem, including also isospin-breaking corrections, to obtain a precision determination consistent with all constraints from analyticity, unitarity, crossing symmetry, and pionic atom-data. Finally, we will perform the matching to chiral perturbation theory in the subthreshold region and detail the consequences for the chiral convergence of the threshold parameters and the nucleon mass.