We will start with the related question of making simple marks in a book to highlight a specific place on the page, which is discussed in classical sources.
The Tur[1] says that it is permitted to make a noticeable impression in a book with one’s fingernail, because the impression does not last. The Bach[2] disagrees because Rabbi Yossi[3] maintains that the etchings made on the beams of the Mishkan were a classic example of kotev (the Torah prohibition of writing on Shabbat), and the lack of permanence only reduces the violation to a Rabbinic level. One strong response to the Bach is that we accept the opinion that disagrees with Rabbi Yossi and holds that a simple mark is forbidden only Rabbinically even when permanent; it is permitted when it is temporary.[4] Other answers are given to lower the issue to no more than a Rabbinic level, which allows outright leniency regarding a temporary situation.[5]
The Shulchan Aruch[6] allows making a mark in a book. The Mishna Berura[7] views the matter more stringently and forbids making a scratch on paper (as opposed to parchment), as the Taz[8] considers this a permanent mark. In our generation, the Yalkut Yosef[9] permits making a mark, whereas the Shemirat Shabbat K’Hilchata[10] forbids it.
Folding a page to help one find the place later is significantly less problematic than making a mark. If one folds the page gently, the pressure of the book may eventually make a line whose impression becomes stronger over time. However, that indirect consequence is likely not considered a violation of Shabbat. Furthermore, even if one presses down hard, his intention is not to make a line, but rather to create the effect of a folded page (which helps both by “thickening” the page and by creating a tab-like indentation at the corner, where the folded part is “missing”). Several authorities[11] maintain that the mark that is left is an example of p’sik reishei d’lo niche lei. In other words, although the ostensibly permitted action that one is doing (folding) causes a definite, direct, forbidden outcome (a line), the forbidden outcome is not desired (one has no interest in having the line). 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.[12] Additional support for leniency is the fact that even purposely making a 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.[13]
It seems that there is a more fundamental reason to permit folding pages. Some actions are inherently quite subjective. An action without a certain level of intent for its outcome is not considered a melacha at all. It makes sense, therefore, to posit that leaving an imprint that is neither a word nor a picture nor anything that conveys a specific content is such an example. In other words, an action has no element of melacha if it does not have significance. Thus, even according to the opinions that the principle that p’sik reishei d’lo niche lei is forbidden applies to Rabbinic violations, folding without intent for the insignificant line is permitted. This thesis can explain why the line that is made when one folds a napkin is not considered writing.[14] Similarly, we note that poskim struggle to explain why it is permitted to walk on soft ground with shoes that have writing on the soles that leave an imprint on the ground.[15] Yet, the question is not even raised about shoes without writing on their soles, despite the fact they also leave a clear imprint on soft ground. Our thesis can explain the difference between these cases.[16]
Thus, for one reason or another, it is quite clear that it is permitted for one to fold the pages of a book on Shabbat in order to hold his place.