i've created a new project and added jQuery just like that:

<head>
<meta charset="utf-8" />
<title>App1</title>

<!-- WinJS references -->
<link href="//Microsoft.WinJS.1.0/css/ui-dark.css" rel="stylesheet" />
<script src="//Microsoft.WinJS.1.0/js/base.js"></script>
<script src="//Microsoft.WinJS.1.0/js/ui.js"></script>

<!-- App1 references -->
<link href="/css/default.css" rel="stylesheet" />
<script src="/js/default.js"></script>
<script src="/js/navigator.js"></script>
<script src="js/jquery-1.8.2-win8-1.0.js"></script>
</head>
and i have error on exit of application.
'WWAHost.exe' (Script): Loaded 'Script Code (MSAppHost/1.0)'.
Exception was thrown at line 5357, column 6 in ms-appx://9639c33e-1eba-439f-9f8f-33d29838c67b/js/jquery-1.8.2-win8-1.0.js
0x800a139e - JavaScript runtime error: SyntaxError
The program '[3500] WWAHost.exe' has exited with code 1 (0x1).

when i continue project instead of that, all jQuery library work fine but WinJS.Application.sessionState doesn't hold data between running appliation.
(I start and stop application according this: http://msdn.microsoft.com/en-us/library/windows/apps/hh986966.aspx#js_tut_suspendandshutdown)