Zero cycles with modulus and zero cycles on singular varieties. (9th October 2017) - Binda, Federico; Krishna, Amalendu
Abstract : Given a smooth varietyX and an effective Cartier divisorDX, we show that the cohomological Chow group of 0-cycles on the double ofX alongD has a canonical decomposition in terms of the Chow group of 0-cyclesCH_0(X) and the Chow group of 0-cycles with modulusCH_0(X|D) onX . WhenX is projective, we construct an Albanese variety with modulus and show that this is the universal regular quotient ofCH_0(X|D) . As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles with modulus. We show thatCH_0(X|D) is torsion-free and there is an injective cycle class mapCH_0(X|D)K_0(X, D) ifX is affine. For a smooth affine surfaceX, this is strengthened to show thatK_0(X, D) is an extension ofCH_1(X|D) byCH_0(X|D) .