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Journals and Conferences
In this paper we present a new and elementary approach for proving the main results of Katz (1996) using the Jordan-Pochhammer matrices of Takano and Bannai (1976) and Haraoka (1994). We nd an explicit version of the middle convolution of Katz (1996) that connects certain tuples of matrices in linear groups. Our approach is valid for elds of any… (More)
In , a purely algebraic analogon of Katz’ middle convolution functor (see ) is given. In this paper, we find an explicit Riemann-Hilbert correspondence for this functor. This leads to a construction algorithm for differential systems which correspond to rigid local systems on the punctured affine line via the Riemann-Hilbert correspondence.
We use the middle convolution to obtain some old and new algebraic solutions of the Painlevé VI equations.
We study 4-dimensional Galois representations attached to Siegel modular forms. In some cases we determine the images of the absolute Galois group. This yields Galois realizations over Qfor projective symplectic groups.
In , a purely algebraic analogon of Katz’ middle convolution functor (see ) is given. It is denoted by MCλ. In this paper, we present a cohomological interpretation of MCλ and find an explicit RiemannHilbert correspondence for this functor. This leads to an algorithm for the construction of Fuchsian systems corresponding to irreducible rigid local… (More)
Using the middle convolution functor MCχ introduced by N. Katz, we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic group G2. We derive the existence of motives for motivated cycles which have a motivic Galois group of type G2. Granting Grothendieck’s standard conjectures, the existence of motives with motivic… (More)
We construct a relative mixed motive whose `-adic realizations give rise to Galois representations of the absolute Galois group of Q whose images are isomorphic to the exceptional groups of Lie-type G2(Z`), if ` is a prime ≥ 5. The method of construction relies on Katz’ motivic description of rigid local systems with quasi-unipotent local monodromy.
In families of Painlevé VI differential equations having common algebraic solutions we classify all the members which come from geometry, i.e. the corresponding linear differential equations which are Picard-Fuchs associated to families of algebraic varieties. In our case, we have one family with zero dimensional fibers and all others are families of… (More)
We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers done by Herfurtner. We also show that pullbacks of hypergeometric functions by rational Belyi functions with restricted ramification data give rise to Heun… (More)