Korach is the parsha of his rebellion against the kehunah and the authority of Moshe over Am Yisrael. This parsha is followed by Chukas which opens up with laws of Parah Adumah. The meforshim ask why did the parsha of ParahAdumah wait until now when it was already told to Yisrael in Marah when they left Mitzrayim (Rashi Shmos 15,25)? You might answer that it was told then to Klal Yisrael but it wasn’t fulfilled until now at Parshas Chukas. The gemarah in Gittin 60 refutes such an answer by stating that this parsha of Para Aduma was said on the day the Mishkan was erected, and the day afterwards they burned the Parah Adumah to make the concoction to purify one who came in contact with a corpse.
We suggest to answer this question by understanding a Medrash (Bamidbar Rabba 18,6) in this parsha. ויפל על פניו  Moshe Rabbeinu fell on his face.

מיד נזדעזע משה מפני המחלוקת מפני שכבר היה בידן סרחון רביעי משל לבן מלך שסרח על אביו ופייס עליו אוהבו פעם שתים ושלש כשסרח רביעית נתרשלו ידי אוהבו של מלך אמר כמה פעמים אטריח את המלך אף כאן משה חטאו בעגל ויחל משה ויהי העם כמתאוננים ויתפלל משה במרגלים ויאמר משה אל ה’ ושמעו מצרים במחלוקתו של קרח אמר כמה אוכל להטריח את המקום לפיכך וישמע משה ויפול על פניו:
Korach claimed that the entire assembly, all of them, are holy and all of them heard at Sinai I am Hashem your G-d.  Had you alone heard this Divine Utterance and the congregation not heard it, you would have reason to say that you are better than us.
Thereupon Moshe became agitated on account of the dispute because the people already now had a fourth strike against them. Moshe’s situation was analogous to that of a king’s son who repeatedly sinned against his father and the king’s dear friend reconciled him once, twice, and even three times. But when the price sinned a fourth time the king’s friend became disheartened. He said to himself how many times can I trouble the king? Here too, when the
people sinned with the Golden Calf  Moshe pleaded before Hashem (Shmos 32,11), afterward when they sinned by complaining Moshe davened on their behalf, with the spies (Bamidbar 14,13) he saved Yisrael from being destroyed. However, with the machlokes of Korach Moshe said How many times can I trouble Hashem. Therefore he fell on his face.
(Also see Rashi  Korach 17,4)
The Aitz Yosef explains this Medrash as follows. Until now Moshe was able to defend Yisrael for their sin of the Golden Calf by claiming that the issur against idolatry was addressed only to him since Hashem had said  לא יהיה לך אלהים אחרים the word lecha is in the singular form. However now that  Korach insisted that Hashem spoke directly to every Yid Moshe could no longer argue that the people were never commanded to abstain from idol worship and thus should not be punished. Moshe therefore became agitated and fearful for Am Yisrael’sfuture for with the Golden Calf in count of Korach’s rebellion, it was Yisrael’sfourth transgression in the desert and regarding of such a string of sins, the passuk say (Iyov 33.29) Behold Hashem atones with man two or three times.
With this Medrash and its explanation, the Maharil Diskin explains a passuk in the beginning of Devarim where Moshe Rabbeinu lists off all the places which there was an episode of Yisrael’s transgression against Hashem. ולבן וחצירות ודי זהב .  The episode of די זהב refers to the Golden Calf because they had an abundance of gold on their hands. The place of חצרות  refers to the machlokesof Korach (see Rashi). The question is that it is out of order for the idolatry of the Golden Calf preceded the rebellion of Korach. He answers with this Medrashthat Hashem forgave Klal Yisrael for the serving of the Golden Calf because of Moshe’s claim that avodah zarah was addressed to Him and not to the people. So there were only three episodes of sin. However, now that Korach claimed that all Yisrael heard the commandment against idolatry, the sin of the Golden Calf returned making it number four of aveiros and Moshe had now nothing to make an appeal to spare them from punishment. That is why the Torah listed after חצרות   the sin of די זהב  ak”l.
With this we can now answer why does the parsha of Parah Aduma follow the parsha of Korach. The answer is that up until now it was forgiven because of Moshe’s defense on Yisrael that the prohibition of avodah zarah was addressed
only to him. However after Korach’s claim that all Yidden heard this issur at HarSinai, the kitrug of the chait Aigel returned and once again the reason for the mitzvah of Parah Adumah that Chazal state was fully applicable (Bamidbar Rabba 19,8). That the Parah Adumah is a tikkun for the Chait Aigel תבוא פרה ותכפר על מעשה העגל
This is analogous to the son of a maidservant who soiled the palace of the king who responded with “Let his mother come and wipe up his excrement”. So too Hashem said let the Parah Adumah come and atone for the sinning of her sonthe Golden Calf.
By the Torah placing Parah Adumah with its details of dinim after Korach, it is conveying that Klal Yisrael needs a new atonement for this resurrected aveirahof avodah zarah because of Korach.

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