Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract $\ell$-adic $1$-motives and Tate's class   In a previous paper we constructed a new class of Iwasawa modules as
$\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motives
in the number field setting. We proved in loc. cit. that the new Iwasawa
modules satisfy an equivariant main conjecture. In this paper we link the new
modules to the $\ell$--adified Tate canonical class, defined by Tate in 1960
and give an explicit construction of (the minus part of) $\ell$--adic Tate
sequences for any Galois CM extension $K/k$ of an arbitrary totally real number
field $k$. These explicit constructions are significant and useful in their own
right but also due to their applications (via our previous results on the
Equivariant Main Conjecture in Iwasawa theory) to a proof of the minus part of
the far reaching Equivariant Tamagawa Number Conjecture for the Artin motive
associated to the Galois extension $K/k$.

3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys