Invariance of plurigenera and Chow-type lemma

Moving Lemma for additive Chow groups and applications

We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of graded-commutative differential graded algebra (CDGA) on these groups.

Chow's moving lemma and the homotopy coniveau tower

We consider the "homotopy coniveau tower" for an arbitrary cohomology theory on smooth varieties over a field or a Dedekind domain. This tower is a generalization of the construction used by Bloch-Lichtenbaum and Friedlander-Suslin in their studies of the spectral sequence from motivic cohomology to K-theory. Our main result is that an application of the classical Chow's moving lemma and some categorical constructions make the homotopy coniveau tower strictly functorial when the base is a field, and functorial in the homotopy category when the base is a Dedekind domain.

A moving lemma for cycles with very ample modulus

We prove a moving lemma for higher Chow groups with modulus, in the sense of Binda-Kerz-Saito, of projective schemes when the modulus is given by a very ample divisor. This provides one of the first cases of moving lemmas for cycles with modulus, not covered by the additive higher Chow groups. We apply this to prove a contravariant functoriality of higher Chow groups with modulus. We use our moving techniques to show that the higher Chow groups of a line bundle over a scheme, with the 0-section as the modulus, vanishes.

A moving lemma for algebraic cycles with modulus and contravariance

We prove a moving lemma which implies the contravariance of Bloch-Esnault's additive higher Chow group in smooth affine varieties and Binda-Saito's higher Chow group (taken in the Nisnevich topology) in smooth varieties equipped with effective Cartier divisors. The new ingredients in the moving method are parallel translation {\em with modulus} in the affine space that involves a new integer parameter, and Noether's normalization lemma over a Dedekind base.

光滑三维与四维簇的自然Chow引理

A natural Chow lemma for smooth threefolds and fourfolds

本文针对维数至多四的光滑真整簇，构造了沿光滑中心的有限爆破序列，以射影端点为终点，并保持所有极大拟射影开集的交集，该构造在函子性主化过程下自然且同构不变。

Suslin's moving lemma with modulus

The moving lemma of Suslin states that a cycle on $X\times \mathbb{A} ^n$ meeting all faces properly can be moved so that it becomes equidimensional over $\mathbb{A}^n$. This leads to an isomorphism of motivic Borel-Moore homology and higher Chow groups. In this short paper we formulate and prove a variant of this. It leads to an isomorphism of Suslin homology with modulus and higher Chow groups with modulus, in an appropriate pro setting.