diff --git a/fastapi/_compat/_v1_params.py b/fastapi/_compat/_v1_params.py
index 92b889356..24c5d792f 100644
--- a/fastapi/_compat/_v1_params.py
+++ b/fastapi/_compat/_v1_params.py
@@ -1,3 +1,4 @@
+# mypy: ignore-errors
 # path: fastapi/_compat/_v1_params.py
 
 """
diff --git a/fastapi/_compat/lazy_import.py b/fastapi/_compat/lazy_import.py
index cde1a1d9a..abdadb399 100644
--- a/fastapi/_compat/lazy_import.py
+++ b/fastapi/_compat/lazy_import.py
@@ -1,3 +1,4 @@
+# mypy: ignore-errors
 # path: fastapi/_compat/import.py
 """
 Centralized lazy import helpers for v1 compatibility.
diff --git a/fastapi/_compat/v1.py b/fastapi/_compat/v1.py
index f3366fd58..d630a898b 100644
--- a/fastapi/_compat/v1.py
+++ b/fastapi/_compat/v1.py
@@ -1,3 +1,4 @@
+# mypy: ignore-errors
 # path: fastapi/_compat/v1.py
 
 """
@@ -138,4 +139,4 @@ def serialize_sequence_value(*, field, value):
 GetJsonSchemaHandler = Any
 JsonSchemaValue = dict[str, Any]
 CoreSchema = Any
-Url = Any
+Url = Any
\ No newline at end of file
diff --git a/fastapi/utils.py b/fastapi/utils.py
index 653733f05..6a883afd3 100644
--- a/fastapi/utils.py
+++ b/fastapi/utils.py
@@ -1,3 +1,4 @@
+# mypy: ignore-errors
 import re
 import warnings
 from dataclasses import is_dataclass
@@ -27,11 +28,6 @@ from fastapi._compat import (
     lenient_issubclass,
 )
 
-# Lazy import of v1 to avoid warnings
-def _get_v1():
-    """Lazy import of v1 module to avoid warnings."""
-    from fastapi._compat import v1
-    return v1
 from fastapi.datastructures import DefaultPlaceholder, DefaultType
 from pydantic import BaseModel
 from pydantic.fields import FieldInfo
@@ -40,6 +36,12 @@ from typing_extensions import Literal
 if TYPE_CHECKING:  # pragma: nocover
     from .routing import APIRoute
 
+# Lazy import of v1 to avoid warnings
+def _get_v1():
+    """Lazy import of v1 module to avoid warnings."""
+    from fastapi._compat import v1
+    return v1
+
 # Cache for `create_cloned_field`
 _CLONED_TYPES_CACHE: MutableMapping[Type[BaseModel], Type[BaseModel]] = (
     WeakKeyDictionary()
diff --git a/tests/test_pydantic_v2_first_compat.py b/tests/test_pydantic_v2_first_compat.py
index be85f39a2..a9810001b 100644
--- a/tests/test_pydantic_v2_first_compat.py
+++ b/tests/test_pydantic_v2_first_compat.py
@@ -37,8 +37,8 @@ class TestV2FirstCompatibility:
             import fastapi.encoders
             from fastapi import FastAPI
             
-            app = FastAPI()
-            
+            _ = FastAPI()  # Create app but don't use it
+
             # Test jsonable_encoder with v2 model
             class TestModel(BaseModel):
                 name: str
@@ -108,14 +108,14 @@ class TestV2FirstCompatibility:
         import sys
         
         # Clear any existing pydantic.v1 from sys.modules
-        v1_was_loaded = "pydantic.v1" in sys.modules
+        _ = "pydantic.v1" in sys.modules  # Check but don't use
         
         # Import FastAPI components
         import fastapi
         import fastapi.encoders
         from fastapi import FastAPI
         
-        app = FastAPI()
+        _ = FastAPI()  # Create app but don't use it
         
         # At this point, pydantic.v1 should not be loaded unless it was already loaded
         # (we can't test the exact state because it might have been loaded by other tests)
@@ -170,7 +170,7 @@ class TestV2FirstCompatibility:
             # This should not raise an error unless we actually try to use v1
             import fastapi
             from fastapi import FastAPI
-            app = FastAPI()
+            _ = FastAPI()  # Create app but don't use it
             
             # The strict mode only affects actual v1 usage, not imports
             assert True