To provide you with a starting point, there are several important issues to keep in mind when using Identity with the ASP.Net kernel:
Frame compatibility
You mentioned that you will use ASP.Net Core, and this can be used with either the .Net Core or the full '.Net Framework (e.g. .Net Framework 4.5.1), which can be specified in your project.json property frameworks .
Microsoft. DocumentDB custom .Net client does not support .Net Core; therefore, you must configure ASP.Net Core to install the "full .Net Framework." If you do not know how to do this, you can create a new project in Visual Studio 2015 and select the project template "ASP.Net Core (.Net Framework)"; project.json will have the framework property properly configured for you.
Identity Version
There are several versions of ASP.Net Identity; remember when choosing a provider that currently refers to an ASP.Net 2.2.1 identifier; however, the latest version 3 , released with ASP.Net Core, is supported by the Microsoft.AspNetCore.Identity 1.0.0 NuGet package, which has some differences and additional features. (Note that this latest package can be used with the full .NET Framework.)
Official implementation
Microsoft decided not to create an official implementation of DocumentDB for ASP.Net Identity, citing the fact that "there are two communities available" (link here )
third party support
Of the available third-party implementations, this Adrian Fernandez is the most widely used one that provides support for ASP.Net Identity 3 using Microsoft's own DocumentDB client. Samples are included in the GitHub repository. ( See below for more details. )
Usage example
An example of using this DocumentDB provider with ASP.Net, including additional features, can be found here .
An additional example of using ASP.Net Core with the Microsoft DocumentDB provider can be found here .
I wrote my own Identity 3 provider for DocumentDB; if I release this on GitHub, I will update this answer with a link.
UPDATE 04/19/2017
For those who are looking for a solution, I now recommend Bernhard Koenig's AspNetCore.Identity.DocumentDb project. It is fully functional, includes unit tests and a sample ASP.Net Core project. Also available through Nuget. It supports netstandard1.6 an net46 .