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We present cosmological constraints for the flat $\Lambda$CDM model,including the sum of neutrino masses, by performing a multi-probe analysis of atotal of 13 tomographic auto- and cross-angular power spectra. This is achievedby combining, at map level, the latest primary CMB and CMB-lensing measurementsfrom the Planck 2018 data release, as well as spectroscopic galaxy samples fromBOSS DR12, and the latest Kilo-Degree Survey (KiDS-1000) tomographic weaklensing shear data release. Our analysis includes auto- and cross-correlationsas well as calibration parameters for all cosmological probes, thus providing aself-calibration of the combined data sets. We find a good fit (reduced$\chi^2$=1.7) for the combined probes with calibration parameters onlymoderately different from their nominal value, thus giving a possibleinterpretation of the tension between the early- and late-Universe probes. Theresulting value for the structure growth parameter is $S_8 = 0.754 \pm 0.016$(68\% CL). We also obtain a $\sim$2.3$\sigma$ constraint on the neutrino masssum of $\sum m_\nu = 0.51^{+0.21}_{-0.24}$ eV (68\% CL), which is compatiblewith current particle physics limits. We perform several tests by fixing theneutrino mass sum to a low value, considering narrower priors on themultiplicative bias parameters for cosmic shear, and by fixing all calibrationparameters to their expected values. These tests result in worse fits comparedto our fiducial run, especially for the case when all calibration parametersare fixed. This latter test also yields a lower upper limit of the neutrinomass sum. We discuss how the interplay between the cosmological and calibrationparameters impact the $S_8$-tension and the constraints on the neutrino masssum. [abridged]

Combined $13\times2$-point analysis of the Cosmic Microwave Background  and Large-Scale Structure: implications for the $S_8$-tension and neutrino  mass constraints