J-PLUS: Unveiling the brightest-end of the Lyα luminosity function at 2.0<z<3.3 over 1000 deg^2

We present the photometric determination of the bright-end (L_Lya>10^43.5 erg/s) of the Lya luminosity function (LF) within four redshifts windows in the interval 2.210^43.3 erg/s) Lya-emitting candidates. We test our selection with two spectroscopic follow-up programs at the GTC telescope, confirming 89 sources, with 64 the first time above L_Lya 10^44 erg/s and down to densities of 10^-8 Mpc^-3. Our results unveil with high detail the Schechter exponential-decay of the brightest-end of the Lya LF, complementing the power-law component of previous LF determinations at 43.32 AGN/QSOs (likely dominant in our samples) are described by a structurally different LF than z>2 star-forming LAEs, namely with L^*_QSOs 100 L^*_LAEs and Phi^*_QSOs 10^-3 Phi^*_LAEs. Finally, our method identifies very efficiently as high-z line-emitters sources without previous spectroscopic confirmation, currently classified as stars ( 2000 objects in each redshift bin, on average). Assuming a large predominance of Lya-emitting AGN/QSOs in our samples, this supports the scenario by which these are the most abundant class of z>2 Lya emitters at L_Lya>10^43.3 erg/s.