Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Integral Part of A-Motivic Cohomology   The deepest arithmetic invariants attached to an algebraic variety defined
over a number field $F$ are conjecturally captured by the integral part of its
motivic cohomology. There are essentially two ways of defining it when $X$ is a
smooth projective variety: one is via the $K$-theory of a regular model, the
other is through its $\ell$-adic realization. Both approaches are conjectured
to coincide. This paper initiates the study of motivic cohomology for global
fields of positive characteristic, hereafter named $A$-motivic cohomology,
where classical mixed motives are replaced by mixed Anderson $A$-motives. Our
main objective is to set the definitions of the model version and the
$\ell$-adic version of the integral part of $A$-motivic cohomology, using
Gardeyn's notion of maximal models of $A$-motives as the analogue of regular
models of varieties. Our main result states that the model version is contained
in the $\ell$-adic version. As opposed to what is expected in the number field
setting, we show that the two approaches do not match in general. We conclude
this work by introducing the submodule of regulated extensions of mixed
Anderson $A$-motives, for which we expect the two approaches to match, and
solve some particular cases of this expectation.

31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph