Can you say the Amidah while the Sefer Torah is being read?

Question

Through an unavoidable circumstance, someone comes to shul late on Shabbos morning.

Despite skipping those parts of the davenning that can be skipped, after saying Shema, he can see that he will be ready to say the Amidah, just as the congregation will start to read from the Sefer Torah.

What considerations are involved and what do the sources advise him to do?

The question could be posed in two cases: (1) where if he delays his Amidah he will miss the time for saying it and (2) where there will be time to say the Amidah after the Torah has been read.

Answer 1

In this site I have found some statements from which I understand that it is not prohibited to pray at the time of the Kriat Hatora, but one need to hear Kriat Hatora after the tefila, because the Kria which was at the time of his tefila is not counted for him:

ומי שאיחר לתפילה, ובשעה שהוא אומר את פסוקי דזמרה או ברכות קריאת שמע, הציבור החל לקרוא בתורה, אם יזדמן לו אח"כ לשמוע את קריאת התורה, ימשיך בתפילתו. אבל אם לא יזדמן לו אח"כ לשמוע את קריאת התורה, לכתחילה טוב שיפסיק מתפילתו וישמע את קריאת התורה (לקט יושר ע' י"ח; יבי"א ז, ט).‏

who arrived late to the prayer, and at the time when they started Kriat Hatora, he still is saying psuke de zimra or birkot Kriat Shema, if he can hear Kriat Hatora afterward, it's best to continue his prayer, but if he should not find an other place to hear Kriat Hatora, Lechatechilla, it's good to interrupt the tefila and to listen the Kriat Hatora.

We see that the question arises only in relation to the obligation of Kriat Hatora, but to pray is not an insult for the Kriat Hatora that is now taking place.

It is also implicit in Shulchan Aruch OC 146, 2:

‏... ויש אומרים שאם יש י' דצייתי (פירוש המשימין לבם) לספר תורה -- מותר לספר (בדברי תורה) (בית יוסף בשם מהרי"א). ויש מתירים למי שתורתו אומנתו. ויש מתירים למי שקודם שנפתח ספר תורה מחזיר פניו ומראה עצמו שאינו רוצה לשמוע ספר תורה אלא לקרות ומתחיל לקרות. ...‏

Others say that, if there are ten men to listen the Kria, it is permitted to talk divre Tora {I assume that to pray is not different}, Some poskim permit only to who is "professionally" involved in Tora. Others allow one who already started to learn before the Kriat Hatora to continue assuming that he indicated that he was not about to listen the Kriat Hatora but to learn, and had already beginning to learn before {I assume also that for prayer, the same rule apply}. But if he is one of the ten men (and there are only ten men) he has to listen.

The source is a Gemara in Berachot 8a.

R' Shesheth used to turn his face to another side and study. He said: We [are busy] with ours, and they [are busy] with theirs.