diff --git a/django/contrib/postgres/fields/array.py b/django/contrib/postgres/fields/array.py
index a76598a9bff4..f867571215f2 100644
--- a/django/contrib/postgres/fields/array.py
+++ b/django/contrib/postgres/fields/array.py
@@ -70,7 +70,7 @@ def check(self, **kwargs):
                 )
             )
         else:
-            base_checks = self.base_field.check()
+            base_checks = self.base_field.check(**kwargs)
             if base_checks:
                 error_messages = "\n    ".join(
                     "%s (%s)" % (base_check.msg, base_check.id)
diff --git a/django/core/checks/registry.py b/django/core/checks/registry.py
index 3139fc3ef4d9..257dadac41b6 100644
--- a/django/core/checks/registry.py
+++ b/django/core/checks/registry.py
@@ -1,6 +1,7 @@
 from collections.abc import Iterable
 from itertools import chain
 
+from django.db import connections
 from django.utils.inspect import func_accepts_kwargs
 
 
@@ -84,6 +85,14 @@ def run_checks(
 
         if tags is not None:
             checks = [check for check in checks if not set(check.tags).isdisjoint(tags)]
+        elif not databases:
+            # By default, 'database'-tagged checks are not run if an alias
+            # is not explicitly specified as they do more than mere static
+            # code analysis.
+            checks = [check for check in checks if Tags.database not in check.tags]
+
+        if databases is None:
+            databases = list(connections)
 
         for check in checks:
             new_errors = check(app_configs=app_configs, databases=databases)
diff --git a/django/db/models/constraints.py b/django/db/models/constraints.py
index 73ab23bdfa94..93251ff322e3 100644
--- a/django/db/models/constraints.py
+++ b/django/db/models/constraints.py
@@ -51,9 +51,12 @@ def remove_sql(self, model, schema_editor):
     def _expression_refs_exclude(cls, model, expression, exclude):
         get_field = model._meta.get_field
         for field_name, *__ in model._get_expr_references(expression):
-            if field_name in exclude:
+            if field_name == "pk":
+                field = model._meta.pk
+            else:
+                field = get_field(field_name)
+            if field_name in exclude or field.name in exclude:
                 return True
-            field = get_field(field_name)
             if field.generated and cls._expression_refs_exclude(
                 model, field.expression, exclude
             ):
diff --git a/tests/check_framework/tests.py b/tests/check_framework/tests.py
index f926308fd78e..138d27aafddd 100644
--- a/tests/check_framework/tests.py
+++ b/tests/check_framework/tests.py
@@ -1,11 +1,11 @@
 import multiprocessing
 import sys
 from io import StringIO
-from unittest import skipIf
+from unittest import mock, skipIf
 
 from django.apps import apps
 from django.core import checks
-from django.core.checks import Error, Warning
+from django.core.checks import Error, Tags, Warning
 from django.core.checks.messages import CheckMessage
 from django.core.checks.registry import CheckRegistry
 from django.core.management import call_command
@@ -92,6 +92,21 @@ def return_non_iterable(**kwargs):
         with self.assertRaisesMessage(TypeError, msg):
             registry.run_checks()
 
+    def test_run_checks_database_exclusion(self):
+        registry = CheckRegistry()
+
+        database_errors = [checks.Warning("Database Check")]
+
+        @registry.register(Tags.database)
+        def database_system_check(**kwargs):
+            return database_errors
+
+        errors = registry.run_checks()
+        self.assertEqual(errors, [])
+
+        errors = registry.run_checks(databases=["default"])
+        self.assertEqual(errors, database_errors)
+
 
 class MessageTests(SimpleTestCase):
     def test_printing(self):
@@ -190,10 +205,12 @@ def tearDown(self):
     def test_simple_call(self):
         call_command("check")
         self.assertEqual(
-            simple_system_check.kwargs, {"app_configs": None, "databases": None}
+            simple_system_check.kwargs,
+            {"app_configs": None, "databases": ["default", "other"]},
         )
         self.assertEqual(
-            tagged_system_check.kwargs, {"app_configs": None, "databases": None}
+            tagged_system_check.kwargs,
+            {"app_configs": None, "databases": ["default", "other"]},
         )
 
     @override_system_checks([simple_system_check, tagged_system_check])
@@ -203,11 +220,17 @@ def test_given_app(self):
         admin_config = apps.get_app_config("admin")
         self.assertEqual(
             simple_system_check.kwargs,
-            {"app_configs": [auth_config, admin_config], "databases": None},
+            {
+                "app_configs": [auth_config, admin_config],
+                "databases": ["default", "other"],
+            },
         )
         self.assertEqual(
             tagged_system_check.kwargs,
-            {"app_configs": [auth_config, admin_config], "databases": None},
+            {
+                "app_configs": [auth_config, admin_config],
+                "databases": ["default", "other"],
+            },
         )
 
     @override_system_checks([simple_system_check, tagged_system_check])
@@ -215,7 +238,8 @@ def test_given_tag(self):
         call_command("check", tags=["simpletag"])
         self.assertIsNone(simple_system_check.kwargs)
         self.assertEqual(
-            tagged_system_check.kwargs, {"app_configs": None, "databases": None}
+            tagged_system_check.kwargs,
+            {"app_configs": None, "databases": ["default", "other"]},
         )
 
     @override_system_checks([simple_system_check, tagged_system_check])
@@ -268,6 +292,17 @@ def test_fail_level(self):
         with self.assertRaises(CommandError):
             call_command("check", fail_level="WARNING")
 
+    def test_database_system_checks(self):
+        database_check = mock.Mock(return_value=[], tags=[Tags.database])
+
+        with override_system_checks([database_check]):
+            call_command("check")
+            database_check.assert_not_called()
+            call_command("check", databases=["default"])
+            database_check.assert_called_once_with(
+                app_configs=None, databases=["default"]
+            )
+
 
 def custom_error_system_check(app_configs, **kwargs):
     return [Error("Error", id="myerrorcheck.E001")]
diff --git a/tests/migrations/test_commands.py b/tests/migrations/test_commands.py
index b5817081d28f..83c5575fd3a8 100644
--- a/tests/migrations/test_commands.py
+++ b/tests/migrations/test_commands.py
@@ -113,7 +113,7 @@ def test_migrate_with_system_checks(self, mocked_check):
         out = io.StringIO()
         call_command("migrate", skip_checks=False, no_color=True, stdout=out)
         self.assertIn("Apply all migrations: migrated_app", out.getvalue())
-        mocked_check.assert_called_once()
+        mocked_check.assert_called_once_with(databases=["default"])
 
     def test_migrate_with_custom_system_checks(self):
         original_checks = registry.registered_checks.copy()
@@ -137,6 +137,25 @@ class CustomMigrateCommandWithSecurityChecks(MigrateCommand):
         command = CustomMigrateCommandWithSecurityChecks()
         call_command(command, skip_checks=False, stdout=io.StringIO())
 
+    @override_settings(
+        INSTALLED_APPS=[
+            "django.contrib.auth",
+            "django.contrib.contenttypes",
+            "migrations.migrations_test_apps.migrated_app",
+        ]
+    )
+    def test_migrate_runs_database_system_checks(self):
+        original_checks = registry.registered_checks.copy()
+        self.addCleanup(setattr, registry, "registered_checks", original_checks)
+
+        out = io.StringIO()
+        mock_check = mock.Mock(return_value=[])
+        register(mock_check, Tags.database)
+
+        call_command("migrate", skip_checks=False, no_color=True, stdout=out)
+        self.assertIn("Apply all migrations: migrated_app", out.getvalue())
+        mock_check.assert_called_once_with(app_configs=None, databases=["default"])
+
     @override_settings(
         INSTALLED_APPS=[
             "migrations",
diff --git a/tests/model_forms/models.py b/tests/model_forms/models.py
index f6c34a35218a..83daa13d71f0 100644
--- a/tests/model_forms/models.py
+++ b/tests/model_forms/models.py
@@ -543,3 +543,22 @@ class Meta:
                 violation_error_message="Price must be greater than zero.",
             ),
         ]
+
+
+class AttnameConstraintsModel(models.Model):
+    left = models.ForeignKey(
+        "self", related_name="+", null=True, on_delete=models.SET_NULL
+    )
+    right = models.ForeignKey(
+        "self", related_name="+", null=True, on_delete=models.SET_NULL
+    )
+
+    class Meta:
+        required_db_features = {"supports_table_check_constraints"}
+        constraints = [
+            models.CheckConstraint(
+                name="%(app_label)s_%(class)s_left_not_right",
+                # right_id here is the ForeignKey's attname, not name.
+                condition=~models.Q(left=models.F("right_id")),
+            ),
+        ]
diff --git a/tests/model_forms/tests.py b/tests/model_forms/tests.py
index f0334e1e8699..129ce56c7ac1 100644
--- a/tests/model_forms/tests.py
+++ b/tests/model_forms/tests.py
@@ -30,6 +30,7 @@
 from .models import (
     Article,
     ArticleStatus,
+    AttnameConstraintsModel,
     Author,
     Author1,
     Award,
@@ -3766,3 +3767,17 @@ def test_check_constraint_refs_excluded_field(self):
         self.assertEqual(
             full_form.errors, {"__all__": ["Price must be greater than zero."]}
         )
+
+    def test_check_constraint_refs_excluded_field_attname(self):
+        left = AttnameConstraintsModel.objects.create()
+        instance = AttnameConstraintsModel.objects.create(left=left)
+        data = {
+            "left": str(left.id),
+            "right": "",
+        }
+        AttnameConstraintsModelForm = modelform_factory(
+            AttnameConstraintsModel, fields="__all__"
+        )
+        full_form = AttnameConstraintsModelForm(data, instance=instance)
+        self.assertFalse(full_form.is_valid())
+        self.assertEqual(full_form.errors, {"right": ["This field is required."]})
diff --git a/tests/postgres_tests/test_array.py b/tests/postgres_tests/test_array.py
index f35211e8ed75..d4289d79dfb3 100644
--- a/tests/postgres_tests/test_array.py
+++ b/tests/postgres_tests/test_array.py
@@ -841,6 +841,25 @@ class MyModel(PostgreSQLModel):
         self.assertEqual(errors[0].id, "postgres.E001")
         self.assertIn("max_length", errors[0].msg)
 
+    def test_base_field_check_kwargs(self):
+        passed_kwargs = None
+
+        class MyField(models.Field):
+            def check(self, **kwargs):
+                nonlocal passed_kwargs
+                passed_kwargs = kwargs
+                return []
+
+        class MyModel(PostgreSQLModel):
+            field = ArrayField(MyField())
+
+        self.assertEqual(MyModel.check(databases=["default"]), [])
+        self.assertEqual(
+            passed_kwargs,
+            {"databases": ["default"]},
+            "ArrayField.check kwargs should be passed to its base_field.",
+        )
+
     def test_invalid_base_fields(self):
         class MyModel(PostgreSQLModel):
             field = ArrayField(