I want to read SGA7. Without considering the others SGA and EGA, Which are the textbooks for monodromy theory?
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2$\begingroup$ Have fun with the bi-extension construction of the monodromy pairing. More seriously, surely you can give some context for your motivation, or indication of what you plan to get out of this "read". There is a huge amount of material in there, insofar as the phrase "monodromy theory" is really too vague to be a baseline for giving meaningful advice. Please offer something more specific about your goals (and some indication of your background would not be irrelevant; e.g., have you read SGA1 and/or SGA2 and what do you know about abelian varieties, Neron models, and p-divisible groups?) $\endgroup$– user27920Commented Jul 24, 2014 at 4:48
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2$\begingroup$ You will need more than textbooks to be able to read SGA 7! Anyway, you may start with the very classical (and beautiful) Singular points of complex hypersurfaces by Milnor (Princeton UP). But be aware that it is a long way from this to SGA 7. $\endgroup$– abxCommented Jul 24, 2014 at 5:51
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3 Answers
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Maybe the following book will be helpful: http://www.springer.com/birkhauser/mathematics/book/978-3-7643-7535-5 (The Monodromy Group, by Henryk Zoladek).
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You may find Illusie's text helpfull: http://gc83.perso.sfr.fr/GTIM/PDF%20GROUPE%20DE%20TRAVAIL/Ducros/Illusie.pdf
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To start with:
Galois Groups and Fundamental Groups, by Tamás Szamuely (The theorem in section 3.4 about the absolute Galois group go $\mathbb{C}(t)$ is amazing and enlightening.)
And then:
Milne, James S. (1980), Étale cohomology, Princeton Mathematical Series 33, Princeton University Press
Deligne, Pierre, ed. (1977), Séminaire de Géométrie Algébrique du Bois Marie — Cohomologie étale (SGA 41⁄2), Lecture notes in mathematics (in French) 569