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Although crop residue returns are extensively practiced in agriculture, large uncertainties remain about greenhouse gas (GHG) emissions and global warming potential (GWP) responses to residue return (RR) rates under different residue placements and nutrient supplements. We conducted a laboratory mesocosm experiment in Alfisol in central India to investigate the responses of soil GHG emissions (CO2, N2O, and CH4) and the global warming potential to four wheat RR rates (R0: no residue; R5: 5 Mg/ha; R10: 10 Mg/ha; R15: 15 Mg/ha) and two placements (surface [Rsur] and incorporated [Rinc]) under three nutrient supplement levels (NSLs) (NS0: no nutrients, NS1: nutrients (N and P) added to balance the stoichiometry of C:N:P to achieve 30% humification in RR at 5 t/ha, NS2: 3 × NS1). The results demonstrated a significant (p < 0.05) interaction effect of RR × NSL × residue placement on N2O emission. However, CH4 and GWP responses to the RR rate were independent of NSL. N2O fluxes ranged from −2.3 µg N2O-N kg−1 soil (R5 NS0 Rsur) to 43.8 µg N2O-N kg−1 soil (R10 NS2 Rinc). A non-linear quadratic model yielded the best fit for N2O emissions with RR rate (R2 ranging from 0.55 to 0.99) in all NSLs and residue placements. Co-applying wheat residue at 10 and 15 Mg/ha at NS1 reduced CH4 and N2O emissions (cf. R0 at NS1). However, increasing NSLs in NS2 reduced the nutrient stoichiometry to < 12:1 (C:N) and < 50:1 (C:P), which increased N2O emissions in all RR rates (cf. R0) across all residue placements. Averaged across nutrient levels and residue placements, the order of the effects of RR rates on CH4 emissions (µg C kg−1 soil) was R10 (5.5) > R5 (3.8) > R15 (2.6) > R0 (1.6). Our results demonstrated a significant linear response of total GWP to RR rates R15 > R10 > R5 > R0, ranging from 201.4 to 1563.6 mg CO2 eq kg−1 soil. In conclusion, quadratic/linear responses of GHGs to RR rates underscore the need to optimize RR rates with nutrient supplements and residue placement to reduce GHG emissions and GWP while ensuring optimal soil health and crop productivity. [ABSTRACT FROM AUTHOR]