I searched so many articles about Bloch-Kato $p$-selmer Groups defined by $p$-adic representation but it seems that $p$ is not necessary to be odd. Hence, I am wondering if it is worth considering Bloch-Kato 2-selmer Groups (2-primary) or Bloch-Kato conjecture for $p=2$ (2 part of Bloch-Kato Conjecture). Besides, there are some papers avoid considering $p=2$ and prove the theorem under the condition $p$ is odd prime.
Thank you very much!
You seem to be asking what the reason is for many papers on $p$-adic Selmer groups to assume throughout that $p > 2$: is because the case $p = 2$ is less interesting, or because it is more difficult?
The answer is definitely the latter. For many theorems concerning p-adic Selmer groups, there is an argument that works to prove the theorem for all sufficiently large primes, but $p = 2$ (and sometimes $p = 3$ as well) present extra difficulties. So it is common to deal with the "generic" cases of large $p$ first, and subsequent papers can then fill in the small primes later. See for instance this paper by Flach, which is devoted to filling in the $p = 2$ case of a theorem proved by Burns and Greither for $p \ge 3$.
