Publications of the Research Institute for Mathematical Sciences

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Volume 49, Issue 4, 2013, pp. 761–800
DOI: 10.4171/PRIMS/119

Published online: 2013-12-04

Hodge Theory of the Middle Convolution

Michael Dettweiler[1] and Claude Sabbah[2]

(1) Universit├Ąt Bayreuth, Germany
(2) Ecole Polytechnique, Palaiseau, France

We compute the behaviour of Hodge data under tensor product with a unitary rank-one local system and middle convolution with a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line.

Keywords: middle convolution, rigid local system, Katz algorithm, Hodge theory, $\ell$-adic representation

Dettweiler Michael, Sabbah Claude: Hodge Theory of the Middle Convolution. Publ. Res. Inst. Math. Sci. 49 (2013), 761-800. doi: 10.4171/PRIMS/119