The influence of the exchange interaction between charge carrier spins and d - electron spins of Mn²⁺ on the magnetoresistance of Hg₁-xMn_XTe semimagnetic semiconductor is theoretically investigated. Transverse and longitudinal magnetoresistances are studied. Analytical expressions for the transverse magnetoresistance depending on the magnetic field magnitude, temperature and band structure parameters, namely exchange interaction constant and band gap, are obtained. It is supposed that the relaxation time is proportional to the density of states, which is calculated taking into account quasilocal acceptor levels. The cases of degenerate and non-degenerate electron gas are considered. It is shown that the exchange interaction essentially influence on the magnetoresistance magnitude. It is obtained that for certain compositions (X) and magnetic field magnitudes transverse magnetoresistance reaches the giant value. It is noted that the magnetoresistance dependence on temperature is determined both the exchange interaction and availability quasilocal acceptor levels.
The longitudinal magnetoresistance of the non-degenerate electron gas weakly depends on exchange interaction. While in the case of degenerate electron gas longitudinal magnetoresistance strongly depends on exchange interaction.
Comparison of the received theoretical dependences with experimental data available in the literature is carried out. The qualitative agreement is received.

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