diff --git a/gdb_arrow.py b/gdb_arrow.py
index 6c3af1680..ad40ec499 100644
--- a/gdb_arrow.py
+++ b/gdb_arrow.py
@@ -304,7 +304,8 @@ def format_timestamp(val, unit):
     seconds, subseconds = divmod(val, traits.multiplier)
     try:
         dt = datetime.datetime.utcfromtimestamp(seconds)
-    except (ValueError, OSError):  # value out of range for datetime.datetime
+    except (ValueError, OSError, OverflowError):
+        # value out of range for datetime.datetime
         pretty = "too large to represent"
     else:
         pretty = dt.isoformat().replace('T', ' ')
diff --git a/src/arrow/io/file.cc b/src/arrow/io/file.cc
index 543fa90a8..3b18bb7b0 100644
--- a/src/arrow/io/file.cc
+++ b/src/arrow/io/file.cc
@@ -36,6 +36,7 @@
 #include <cerrno>
 #include <cstdint>
 #include <cstring>
+#include <limits>
 #include <memory>
 #include <mutex>
 #include <sstream>
@@ -560,17 +561,22 @@ class MemoryMappedFile::MemoryMap
       RETURN_NOT_OK(::arrow::internal::FileTruncate(file_->fd(), initial_size));
     }
 
-    size_t mmap_length = static_cast<size_t>(initial_size);
-    if (length > initial_size) {
-      return Status::Invalid("mapping length is beyond file size");
-    }
-    if (length >= 0 && length < initial_size) {
+    int64_t mmap_length = initial_size;
+    if (length >= 0) {
       // memory mapping a file region
-      mmap_length = static_cast<size_t>(length);
+      if (length > initial_size) {
+        return Status::Invalid("mapping length is beyond file size");
+      }
+      mmap_length = length;
+    }
+    if (static_cast<int64_t>(static_cast<size_t>(mmap_length)) != mmap_length) {
+      return Status::CapacityError("Requested memory map length ", mmap_length,
+                                   " does not fit in a C size_t "
+                                   "(are you using a 32-bit build of Arrow?");
     }
 
-    void* result = mmap(nullptr, mmap_length, prot_flags_, map_mode_, file_->fd(),
-                        static_cast<off_t>(offset));
+    void* result = mmap(nullptr, static_cast<size_t>(mmap_length), prot_flags_, map_mode_,
+                        file_->fd(), static_cast<off_t>(offset));
     if (result == MAP_FAILED) {
       return Status::IOError("Memory mapping file failed: ",
                              ::arrow::internal::ErrnoMessage(errno));