In Deligne's paper on his first proof of the Weil conjectures, we have the following result.



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> **Theorem 5.10 (Kazhdan-Margulis).** *L'image de $\rho: \pi\_1(U, u) \to \text{Sp}(E/(E \cap E^\perp), \psi)$ est ouverte.*
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This theorem says the monodromy group of a Lefschetz pencil of odd fiber dimension is "as big as possible".


My question is, where has this proof been written down in the literature? I'm finding the discussion in Deligne to be quite terse, and I searched the papers of Kazhdan and Marguilis and I couldn't find a paper which establishes this result.



Reference result: proof of theorem of Kazhdan-Margulis on monodromy group of a Lefschetz pencil of odd fiber dimenion is "as big as possible"
The proof of this result is worked out in detail in page 250 (theorem 7.5) of the book


* Eberhard Freitag, Reinhardt Kiehl "Etale Cohomology and the Weil Conjecture"


You can preview that page in particular [here](https://books.google.es/books?id=PZv6CAAAQBAJ&pg=PA250#v=onepage&q&f=false).


