arXiv subjects

Michael Dettweiler

Publications and source records attributed to Michael Dettweiler.

20 records · Page 2Linked to original sources

arXiv2004

Variation of local systems and parabolic cohomology

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.

math.AG↗

arXiv2003

On the middle convolution

We present a cohomological interpretation of the middle convolution functor MC and find an explicit Riemann-Hilbert correspondence for MC_λ. This leads to an algorithm for the construction of Fuchsian systems which correspond to irreducible rigid local systems under the Riemann-Hilbert correspondence. Also, the effect of MC_λon the p-curvatures ist determined and new examples of differential systems are found which satisfy the Grothendieck-Katz p-curvature conjecture.

math.AG↗