Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weil-\'{e}tale cohomology and duality for arithmetic schemes in negative
  weights   Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560)
Weil-\'etale cohomology $H^i_\text{W,c} (X, \mathbb{Z} (n))$ for a proper,
regular arithmetic scheme $X$ (i.e. separated and of finite type over
$\operatorname{Spec} \mathbb{Z}$) and $n \in \mathbb{Z}$. In the case when $n <
0$, we generalize their construction to an arbitrary arithmetic scheme $X$,
thus removing the proper and regular assumption. The construction assumes
finite generation of suitable \'etale motivic cohomology groups.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat