Handle all dtypes in convert_dtypes

python/cudf/cudf/core/groupby/groupby.py

@@ -1284,6 +1284,27 @@ def _wrap_idxmin_idxmax(self, result: DataFrame | Series, *, skipna: bool):
             raise ValueError(
                 "Encountered all NA values in a group with skipna=True"
             )
+        # idxmin/idxmax return positional/label indices, which take their
+        # dtype from the source object's row index — not from the values
+        # being reduced. Cast the (non-key) result columns accordingly to
+        # match pandas, where reducing an Int64 column still yields int64
+        # indices for a default RangeIndex. Skip the cast when the source
+        # uses a MultiIndex (no single representative dtype) to avoid
+        # lossy/unsupported casts.
+        from cudf.core.multiindex import MultiIndex
+
+        if isinstance(self.obj.index, MultiIndex):
+            return result
+        index_dtype = self.obj.index.dtype
+        key_names = set(self.grouping.names)
+        if result.ndim == 2:
+            for name, col in result._column_labels_and_values:
+                if name in key_names:
+                    continue
+                if col.dtype != index_dtype:
+                    result._data[name] = col.astype(index_dtype)
+        elif result.dtype != index_dtype:
+            result = result.astype(index_dtype)
         return result
 
     def _reduce_numeric_only(self, op: str):