Can't get claims from JWT token with ASP.NET Core

I'm trying to do a really simple implementation of JWT bearer authentication with ASP.NET Core. I return a response from a controller a bit like this:

    var identity = new ClaimsIdentity();
    identity.AddClaim(new Claim(ClaimTypes.Name, applicationUser.UserName));
        var jwt = new JwtSecurityToken(
             _jwtOptions.Issuer,
             _jwtOptions.Audience,
             identity.Claims,
             _jwtOptions.NotBefore,
             _jwtOptions.Expiration,
             _jwtOptions.SigningCredentials);

       var encodedJwt = new JwtSecurityTokenHandler().WriteToken(jwt);

       return new JObject(
           new JProperty("access_token", encodedJwt),
           new JProperty("token_type", "bearer"),
           new JProperty("expires_in", (int)_jwtOptions.ValidFor.TotalSeconds),
           new JProperty(".issued", DateTimeOffset.UtcNow.ToString())
       );

I have Jwt middleware for incoming requests:

app.UseJwtBearerAuthentication(new JwtBearerOptions
{
     AutomaticAuthenticate = true,
     AutomaticChallenge = true,
     TokenValidationParameters = tokenValidationParameters
});

This seems to work to protect resources with the authorize attribute, but the claims never show up.

    [Authorize]
    public async Task<IActionResult> Get()
    {
        var user = ClaimsPrincipal.Current.Claims; // Nothing here

You can't use ClaimsPricipal.Current in an ASP.NET Core application, as it's not set by the runtime. You can read https://github.com/aspnet/Security/issues/322 for more information.

Instead, consider using the User property, exposed by ControllerBase.

Access User.Claims instead of ClaimsPrinciple.Current.Claims.

From Introduction to Identity at docs.asp.net:

...inside the HomeController.Index action method, you can view the User.Claims details.

Here is the relevant source code from the MVC repository:

public ClaimsPrincipal User
{
   get
   {
       return HttpContext?.User;
   }
}