2017
DOI: 10.1112/s0010437x17007503
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Zero cycles with modulus and zero cycles on singular varieties

Abstract: Given a smooth variety X and an effective Cartier divisor D ⊂ X, we show that the cohomological Chow group of 0-cycles on the double of X along D has a canonical decomposition in terms of the Chow group of 0-cycles CH0(X) and the Chow group of 0cycles with modulus CH0(X|D) on X. When X is projective, we construct an Albanese variety with modulus and show that this is the universal regular quotient of CH0(X|D).As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles wit… Show more

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Cited by 40 publications
(146 citation statements)
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References 47 publications
(126 reference statements)
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“…If d ≤ 2, then part (2) of the above theorem holds without any condition on D and this was shown in [6]. If k is not necessarily algebraically closed, we can prove the following.…”
Section: 2mentioning
confidence: 76%
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“…If d ≤ 2, then part (2) of the above theorem holds without any condition on D and this was shown in [6]. If k is not necessarily algebraically closed, we can prove the following.…”
Section: 2mentioning
confidence: 76%
“…The crucial ingredient here is the Roitman torsion theorem of [25]. We derive Bloch's formula in the modulus setting using this and a decomposition theorem for the Chow group of 0-cycles from [6]. In this section, we also prove Theorems 1.6 and 1.7.…”
Section: 2mentioning
confidence: 95%
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“…The Chow group CH LW 0 (X) was discovered by Levine and Weibel [31] in an attempt to describe the Grothendieck group of a singular scheme in terms of algebraic cycles. The modified version CH BK 0 (X) was introduced in [4].…”
Section: Lifting Of Zero-cyclesmentioning
confidence: 99%