GUIDE Install ICS (Ice Cream Sandwich) on Xperia ™ Smartphones, Root and Downgrade Gingerbread
Main: {GUIDE} How to Install Jelly Bean , ICS ( Ice Cream Sandwich) and Gingerbread on Xperia™ Smartphones, as well as root them

This Post Xperias. For 2012 Xperia
How to Root 4.0.3
Just follow the instructions here.
Rooting:
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If you face a problem in downloading the tool, then here is Rooting Toolkit
How to eradicate 4.0.4 (4.1.B.0.587 and 4.1.B.0.431)
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Follow all steps please
Go to Settings> Security> Check "unknown sources"
Configuration> Developer> USB Debugging Mark
Settings> Xperia> Connectivity> USB Connection Mode> select MSC mode
You have to have the Flash Tool:
Flashtool - Xperia devices flashing

1) Download the relevant core to 4.1.A.0.562 Flashing:

Arc y Arc S - Kernel
http://adf.ly/1249456/http://www.4shared...ernel.html
Ray - Kernel
http://adf.ly/1249456/http://www.4shared...ernel.html
Neo / Neo V - Kernel
http://adf.ly/1249456/http://www.4shared...ernel.html
LWW, Mini - Kernel
http://adf.ly/1249456/http://www.4shared...ernel.html
Activo - Kernel
http://adf.ly/1249456/http://www.4shared...ernel.html

2) Go to C :/ Drive> FlashTool> firmware> present everything delete and put the kernel

3) Execute FlashTool click the Flash icon (left side under "file")
Select Flashmode> ok
Installation should be like> select OK

[Image: Kernel + setup.png]

Follow the steps to connect the phone and flash.
FlashTool can display error after flashing kernel, do not worry. Even the build number, Android version will not change. Everything would be the same. So please do not go to your phone settings to check anything.

4) After flashing, reset the device can not start completely, can stay in the Sony logo or white / black.
Whatever the state is just restart the device and continue the rooting.

(Be sure to close FlashTool before running the toolkit rooteo)
Now connect your phone to your PC and phone Root
If you face a problem downloading the tools, then here is Rooting Toolkit
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5) Kernels download, if you are in 4.1.b.0.431 rom then download the respective core, same goes for 4.1.B.0.587
Xperia

4.1.B.0.431
4.1.B.0.587
Arco SKernelKernel
http://adf.ly/1249456/http://www.4shared...ernel.html
Arco KernelKernel
http://adf.ly/1249456/http://www.4shared...ernel.html
ray KernelKerne
http://adf.ly/1249456/http://www.4shared...ernel.html
lNeoKernelKernel
http://adf.ly/1249456/http://www.4shared...ernel.html
VKernelKernel Neo
http://adf.ly/1249456/http://www.4shared...ernel.html
Mini KernelKerne
http://adf.ly/1249456/http://www.4shared...ernel.html
lProKernelKernel
http://adf.ly/1249456/http://www.4shared...K_KER.html
Vive con walkmanKernelKernel
http://adf.ly/1249456/http://www.4shared...furl=d1url
ActiveKernelKernel
http://adf.ly/1249456/http://www.4shared...431_K.html
ProKernelKernel Mini
http://adf.ly/1249456/http://www.4shared...ernel.html

Now flash the kernel (the same procedure as in step 2 and 3)
Your cellphone is rooteado (will see Superuser application is installed on the phone)
To flash the 4.0.2.A.0.42 firmware or any, follow this guide