Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the local Tamagawa number conjecture for Tate motives over tamely
  ramified fields   The local Tamagawa number conjecure, first formulated by Fontaine and
Perrin-Riou, expresses the compatibility of the (global) Tamagawa number
conjecture on motivic $L$-functions with the functional equation. The local
conjecture was proven for Tate motives over finite unramified extensions
$K/\mathbb{Q}_p$ by Bloch and Kato. We use the theory of $(\phi,
\Gamma_K)$-modules and a reciprocity law due to Cherbonnier and Colmez to
provide a new proof in the case of unramified extensions, and to prove the
conjecture for the motive $\mathbb{Q}_p(2)$ over certain tamely ramified
extensions.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin