Is earth's mantle part of the biosphere? why or why not?

Biosphere is the part of the earth where life exists.

the temperature in the mantle is too hot to sustain life.

hence it is not a part of biosphere.

The biosphere is the biological component of earth systems, which also include the lithosphere, hydrosphere, atmosphere. The biosphere includes all living organisms on earth, together with the dead organic matter produced by them. Mantle is a layer of earth which lies below the crust and has high temperature and pressure conditions. No living organism can survive in the mantle so mantle is not a part of Biosphere.