Variation of local systems and parabolic cohomology

Details Variation of local systems and parabolic cohomology Variation of local systems and parabolic cohomology

2003-10-09

arxiv.org/abs/math/0310139v2

Mathematics

Algebraic Geometry

28 pages, 1 figure

Scientific paper

Given a family of local systems on a punctured Riemann sphere, with moving singularities, its first parabolic cohomology is a local system on the base space. We study this situation from different points of view. For instance, we derive universal formulas for the monodromy of the resulting local system. We use a particular example of our construction to prove that the simple groups $\PSL_2(p^2)$ admit regular realizations over the field $\QQ(t)$ for primes $p\not\equiv 1,4,16\mod{21}$. Finally, we compute the monodromy of the Euler-Picard equation, reproving a classical result of Picard.

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