The Künneth Formula for the Twisted de Rham and Higgs Cohomologies

Kai-Chieh Chen^a, Jeng-Daw Yu<sup>b

a</sup> Department of Mathematics, University of California, Berkeley, Berkeley, CA, USA
^b Department of Mathematics, National Taiwan University, Taipei, Taiwan

Abstract: We prove the Künneth formula for the irregular Hodge filtrations on the exponentially twisted de Rham and the Higgs cohomologies of smooth quasi-projective complex varieties. The method involves a careful comparison of the underlying chain complexes under a certain elimination of indeterminacy.

Keywords: de Rham complex; Hodge filtration; Künneth formula.

MSC: 14F40; 18F20; 14C30

Received: February 23, 2018; in final form June 2, 2018; Published online June 12, 2018

Language: English

DOI: 10.3842/SIGMA.2018.055

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