Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicities in Selmer groups and root numbers for Artin twists   Let $K/F$ be a finite Galois extension of number fields and $\sigma$ be an
absolutely irreducible, self-dual representation of $\mathrm{Gal}(K/F)$. Let
$p$ be an odd prime and consider two elliptic curves $E_1, E_2$ with good,
ordinary reduction at primes above $p$ and equivalent mod-$p$ Galois
representations. In this article, we study the variation of the parity of the
multiplicities of $\sigma$ in the representation space associated to the
$p^\infty$-Selmer group of $E_i$ over $K$. We also compare the root numbers for
the twist of $E_i/F$ by $\sigma$ and show that the $p$-parity conjecture holds
for the twist of $E_1/F$ by $\sigma$ if and only if it holds for the twist of
$E_2/F$ by $\sigma$. We also express Mazur-Rubin-Nekov\'a\v{r}'s arithmetic
local constants in terms of certain local Iwasawa invariants.

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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex