Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A finer Tate duality theorem for local Galois symbols   Let $K$ be a finite extension of $\mathbb{Q}_p$. Let $A$, $B$ be abelian
varieties over $K$ of good reduction. For any integer $m\geq 1$, we consider
the Galois symbol $K(K;A,B)/m\rightarrow H^2(K,A[m]\otimes B[m])$, where
$K(K;A,B)$ is the Somekawa $K$-group attached to $A,B$. This map is a
generalization of the Galois symbol $K_2^M(K)/m\rightarrow H^2(K,\mu_m^{\otimes
2})$ of the Bloch-Kato conjecture, where $K_2^M(K)$ is the Milnor $K$-group of
$K$. In this paper we give a geometric description of the image of this
generalized Galois symbol by looking at the Tate duality pairing
$H^{2}(K,A[m]\otimes
B[m])\times\mathrm{Hom}_{G_{K}}(A[m],B^{\star}[m])\rightarrow\mathbb{Z}/m,$
where $B^\star$ is the dual abelian variety of $B$. Under this perfect pairing
we compute the exact annihilator of the image of the Galois symbol in terms of
an object of integral $p$-adic Hodge theory.

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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas