A decomposition theorem for 0-cycles and applications to class field theory

Bertini theorems revisited

“…In such cases, one needs very general Bertini theorems for quasi‐projective schemes over discrete valuation rings. When the model is smooth, a Bertini theorem of this kind has already played a key role in the proof of [22, Lemma 13.2]. Our hope is that the general Bertini theorem of this paper will be very useful in the study of class field theory of regular varieties over local fields of positive characteristics.…”

“…Over such a field, we also often need Bertini theorems for other properties such as reducedness and integrality. For instance, the Bertini theorems of this paper (for regularity, reducedness, and integrality) over imperfect fields are crucially used in the proof of [21, Lemma 3.2, p. 12].…”

Suslin homology via cycles with modulus and applications

“…We use the decomposition theorem of [22] as first of the key tools. This result provides an injective homomorphism p * ∶ CH 0 (X|D) → CH l.c.i.…”