Project description

The main long term aim of this proposal is the construction of realisation functors on the category of motives with values in Saito's derived category of mixed Hodge modules and in a yet to be defined p-adic version. We propose to use homotopic and motivic methods, most notably infinity categories and the h-topology.

Related publications

Published articles

F. Hörmann, Fibered Derivators and (co)homological descent, Theory Appl. Categ., Vol. 32, 2017, No. 38, pp 1258--1362.

F. Hörmann, Six-Functor-Formalisms and Fibered Multiderivators, Selecta Mathematica, 24(4), pp. 2841--2925 (2018)

F. Hörmann, Enlargement of (fibered) derivators, J. Pure Applied Algebra 224 (2020), pp. 1023--1063

F. Hörmann, Descent for coherent sheaves along formal/open coverings, C. R. Math. Acad. Sci. Paris, 358, no. 5, 577-594.

S. Kelly, S. Saito, Smooth blowup square for motives with modulus, Bulletin Polish Acad. Sci. Math. (2020)

Preprints

B. Drew, Motivic Hodge modules, Preprint 2018, arXiv:1801.10129.

B. Drew, M. Gallauer, The universal six-functor formalism, Preprint 2020. arXiv:2009.13610.

F. Hörmann, Derivator Six-Functor-Formalisms---Definition and Construction I, 52 p. preprint 2017. arXiv:1701.02152.

F. Hörmann, M. Wendt, 2018 Derivators and tilting. 12 p. , Appendix to W. Soergel; R. Virk; M. Wendt, Equivariant motives and geometric representation theory, preprint 2018. arXiv:1809.05480.

F. Hörmann, Derivator Six-Functor-Formalisms---Construction II, preprint 2019, arXiv:1902.03625.

F. Hörmann, Model category structures on simplicial objects, Preprint 2021, arXiv:2103.01156.