AJAX is a term coined long ago to represent a feature of modern browsers by which asynchronous HTTP requests can be done, via JavaScript or by the browser, without a full page reload.
ASP.NET Core does not offer any support for AJAX, which doesn't mean that you can't use it—it is just the case that you need to do it manually.
The following example uses jQuery to retrieve values in a form and send them to an action method. Make sure the jQuery library is included in either the view file or the layout:
<form>
<fieldset>
<div><label for="name">Name: </label></div>
<div><input type="text" name="name" id="name" />
<div><label for="email">Email: </label></div>
<div><input type="email" name="email" id="email" />
<div><label for="...