An easy way to keep a bookmark is to fold the upper-right corner of a book (aka Dog ears)
Is such an action permitted on Shabbos?
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Based on Shmirat Shabat Kehilchata Ch: 28, 16, we are allowed to fold papers but not to make toys/games, because in the case of the toys you are making a kli. The previous point (28, 15) deals on the issur of making marks, even with the nail. The example brought is to know where we are in a book.
HaGaon HaRab Mutzafi Shelita says it is not proper to fold pages of Sifre Kodesh. Here is the Lashon:
קיפול דף מנהג גרוע ולא מתאים לספר קדוש
"The folding of pages is a bad custom and is not proper for holy book."
If during the week it is Asur, it is also on Shabbat.
HaRav Yishak Yosef writes straight out in Yalkut Yosef that it is Mutar.
I researched this after asking myself the question on Shabbat and found the answers on this page somewhat confusing -- partly due to the fact that some answers address making a mark (which the Shmirat Shabbat forbids but Yalkut Yosef permits) while the question is on folding the corner of a book.
In a comprehensive survey of the issue, R Daniel Mann from Eretz Hemda concludes folding the corner of a page is definitely permitted. To quote the core of his argument
Certainly, if one folds the page gently, even if the pressure on the book makes the line impression stronger over time, that indirect consequence is likely not considered a violation of Shabbat. However, even if one presses down hard, his intention is not to make a line but to create the effect of a folded page (which helps both by "thickening" the page and creating a tab-like indentation at the corner where the folded part is "missing.")
Several authorities (including Yalkut Yosef 340:6) say this is an example of p’sik reishei d’lo niche lei. In other words, although the ostensibly permitted action that one is doing (folding) includes a definite, direct, forbidden outcome (a line), the forbidden outcome is not desired (one has no interest in having a line after unfolding the page). While most poskim forbid p’sik reishei d’lo niche lei, many say it is permitted when the violation is only Rabbinic in the first place. (See Yabia Omer V, OC 28, who is lenient. The Mishna Berura 314:11 is among many who generally rule stringently).
In our case, the situation is even more lenient, as even purposely making the mark is permitted according to many important authorities. Therefore, it is not surprising that the consensus of poskim is that it is permitted to fold the page (see Yalkut Yosef 340:6.; Shemen Afarsimon 7; Piskei Teshuvot 340:19).
See also here from dinonline. They specifically address the possible concern of hachana (prohibition to prepare on Shabbat for the week) and write "regarding hachana, that is also not a problem because it might be needed for today as there is a possibility that you might want to look it up again."
The Shulchan Aruch 340:5 writes that one can mark a sefer with one’s nail since it isn’t something which lasts. However, the Magen Avraham notes that the Mahrshal differentiates between klaf (parchment) and regular paper. Parchment being mutar since it’s a hard material and paper which is soft should be assur since the marking is something which will last. The Shevet Hakehasi explains that bending the corner of the page of a book is different since one doesn’t need the crease rather one wants the corner to be bent so he knows what page they were on. He concludes that it is mutar. [He notes that Rav Tzadok Hakohen from Lublin was makpid not to bend the corners of any of his seforim because of the kavod of the seferoim]. (Shevet Hakehasi 1:130)