diff --git a/swh/deposit/api/checks.py b/swh/deposit/api/checks.py
--- a/swh/deposit/api/checks.py
+++ b/swh/deposit/api/checks.py
@@ -5,15 +5,14 @@
 
 """Functional Metadata checks:
 
-Mandatory fields:
-- 'author'
-- 'name' or 'title'
+Mandatory alternate fields:
+- 'author' or 'codemeta:author'
+- 'name' or 'codemeta:name' or 'title' or 'codemeta:title'
 
 """
 
 from typing import Dict, Optional, Tuple
 
-MANDATORY_FIELDS_MISSING = "Mandatory fields are missing"
 ALTERNATE_FIELDS_MISSING = "Mandatory alternate fields are missing"
 
 
@@ -28,36 +27,26 @@
           ok (False, <detailed-error>) otherwise.
 
     """
-    # following fields are mandatory
-    required_fields = {
-        "author": False,
-    }
     # at least one value per couple below is mandatory
-    alternate_fields = {
-        ("name", "title"): False,
+    mandatory_alternate_fields = {
+        ("codemeta:author", "author"): False,
+        ("name", "title", "codemeta:name", "codemeta:title"): False,
     }
 
     for field, value in metadata.items():
-        for name in required_fields:
-            if name in field:
-                required_fields[name] = True
-
-        for possible_names in alternate_fields:
+        for possible_names in mandatory_alternate_fields:
             for possible_name in possible_names:
                 if possible_name in field:
-                    alternate_fields[possible_names] = True
+                    mandatory_alternate_fields[possible_names] = True
                     continue
 
-    mandatory_result = [k for k, v in required_fields.items() if not v]
-    optional_result = [" or ".join(k) for k, v in alternate_fields.items() if not v]
+    alternate_fields_result_check = [
+        " or ".join(k) for k, v in mandatory_alternate_fields.items() if not v
+    ]
 
-    if mandatory_result == [] and optional_result == []:
+    if alternate_fields_result_check == []:
         return True, None
-    detail = []
-    if mandatory_result != []:
-        detail.append({"summary": MANDATORY_FIELDS_MISSING, "fields": mandatory_result})
-    if optional_result != []:
-        detail.append(
-            {"summary": ALTERNATE_FIELDS_MISSING, "fields": optional_result,}
-        )
+    detail = [
+        {"summary": ALTERNATE_FIELDS_MISSING, "fields": alternate_fields_result_check,}
+    ]
     return False, {"metadata": detail}
diff --git a/swh/deposit/tests/api/test_checks.py b/swh/deposit/tests/api/test_checks.py
--- a/swh/deposit/tests/api/test_checks.py
+++ b/swh/deposit/tests/api/test_checks.py
@@ -23,6 +23,30 @@
             "title": "bar",
             "author": "no one",
         },
+        {
+            "url": "some url",
+            "external_identifier": "some id",
+            "title": "bar",
+            "codemeta:author": "no one",
+        },
+        {
+            "url": "some url",
+            "external_identifier": "some id",
+            "codemeta:title": "bar",
+            "codemeta:author": "no one",
+        },
+        {
+            "url": "some url",
+            "external_identifier": "some id",
+            "codemeta:name": "bar",
+            "codemeta:author": "no one",
+        },
+        {
+            "url": "some url",
+            "external_identifier": "some id",
+            "name": "bar",
+            "codemeta:author": "no one",
+        },
     ],
 )
 def test_api_checks_check_metadata_ok(metadata_ok, swh_checks_deposit):
@@ -42,7 +66,7 @@
             },
             {
                 "summary": "Mandatory alternate fields are missing",
-                "fields": ["name or title"],
+                "fields": ["name or title or codemeta:name or codemeta:title"],
             },
         ),
         (
@@ -51,7 +75,53 @@
                 "external_identifier": "something-else",
                 "title": "foobar",
             },
-            {"summary": "Mandatory fields are missing", "fields": ["author"],},
+            {
+                "summary": "Mandatory alternate fields are missing",
+                "fields": ["codemeta:author or author"],
+            },
+        ),
+        (
+            {
+                "url": "something",
+                "external_identifier": "something-else",
+                "name": "foobar",
+            },
+            {
+                "summary": "Mandatory alternate fields are missing",
+                "fields": ["codemeta:author or author"],
+            },
+        ),
+        (
+            {
+                "url": "something",
+                "external_identifier": "something-else",
+                "codemeta:title": "foobar",
+            },
+            {
+                "summary": "Mandatory alternate fields are missing",
+                "fields": ["codemeta:author or author"],
+            },
+        ),
+        (
+            {
+                "url": "something",
+                "external_identifier": "something-else",
+                "codemeta:name": "foobar",
+            },
+            {
+                "summary": "Mandatory alternate fields are missing",
+                "fields": ["codemeta:author or author"],
+            },
+        ),
+        (
+            {"url": "something", "external_identifier": "something-else",},
+            {
+                "summary": "Mandatory alternate fields are missing",
+                "fields": [
+                    "codemeta:author or author",
+                    "name or title or codemeta:name or codemeta:title",
+                ],
+            },
         ),
     ],
 )
diff --git a/swh/deposit/tests/api/test_deposit_private_check.py b/swh/deposit/tests/api/test_deposit_private_check.py
--- a/swh/deposit/tests/api/test_deposit_private_check.py
+++ b/swh/deposit/tests/api/test_deposit_private_check.py
@@ -7,7 +7,7 @@
 import pytest
 from rest_framework import status
 
-from swh.deposit.api.checks import ALTERNATE_FIELDS_MISSING, MANDATORY_FIELDS_MISSING
+from swh.deposit.api.checks import ALTERNATE_FIELDS_MISSING
 from swh.deposit.api.private.deposit_check import (
     MANDATORY_ARCHIVE_INVALID,
     MANDATORY_ARCHIVE_MISSING,
@@ -130,13 +130,15 @@
         assert len(details["archive"]) == 1
         assert details["archive"][0]["summary"] == MANDATORY_ARCHIVE_UNSUPPORTED
         # metadata check failure
-        assert len(details["metadata"]) == 2
-        mandatory = details["metadata"][0]
-        assert mandatory["summary"] == MANDATORY_FIELDS_MISSING
-        assert set(mandatory["fields"]) == set(["author"])
-        alternate = details["metadata"][1]
-        assert alternate["summary"] == ALTERNATE_FIELDS_MISSING
-        assert alternate["fields"] == ["name or title"]
+        assert details["metadata"] == [
+            {
+                "summary": ALTERNATE_FIELDS_MISSING,
+                "fields": [
+                    "codemeta:author or author",
+                    "name or title or codemeta:name or codemeta:title",
+                ],
+            }
+        ]
 
         deposit = Deposit.objects.get(pk=deposit.id)
         assert deposit.status == DEPOSIT_STATUS_REJECTED
diff --git a/swh/deposit/tests/api/test_deposit_update.py b/swh/deposit/tests/api/test_deposit_update.py
--- a/swh/deposit/tests/api/test_deposit_update.py
+++ b/swh/deposit/tests/api/test_deposit_update.py
@@ -799,7 +799,7 @@
     assert response.status_code == status.HTTP_400_BAD_REQUEST
     assert b"Functional metadata checks failure" in response.content
     # detail on the errors
-    assert b"- Mandatory fields are missing (author)" in response.content
     assert (
-        b"- Mandatory alternate fields are missing (name or title)" in response.content
+        b"- Mandatory alternate fields are missing (codemeta:author or author, "
+        b"name or title or codemeta:name or codemeta:title)" in response.content
     )