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Let $X$ be an Artin stack and $Z \subset X$ be a closed substack. Can we represent $Z$ as a fundamental cycle? i.e. $[Z] = \sum_i a_i [Z_i]$ where $Z_i$ are integral substacks of $X$. In other word, c …

I'm reading the construction of difference bundle(generalized) in the paper of Atiyah-Hirzebruch(Analytic cycles on complex manifolds) There is one thing I cannot understand. The followings are in th …

There is an analogy of Chow's lemma for a DM stack $X$ written in the Laumon's book 'Champ algebrique'. There exists a generically finite, proper surjective morphism $Y \to X$ from a quasi-projective …

Assume $X$ is a subscheme of $Y$ and $X,Y$ are irreducible. Then every irreducible component of the normal cone $C_{X/Y}$ dominates $X$?

I'm reading Andrew Kresch's paper, Cycle groups in Artin Stacks. The author defined Chow groups of Artin stacks by very technical way, instead of ordinary ways which he called 'naive chow group', quo …