Research publications

Ben Moonen A remark on the Tate conjecture. Preprint, September 2017, 3 pages. (Submitted)
Ben Moonen Families of Motives and the Mumford-Tate Conjecture. Milan J. of Math., 2017.
Ben Moonen The Deligne-Mostow list and special families of surfaces. IMRN, 2017. Erratum and addendum.
Anna Cadoret and Ben Moonen Integral and adelic aspects of the Mumford-Tate conjecture. Preprint, August 2015. (Submitted)
Ben Moonen On the Tate and Mumford-Tate conjectures in codimension one for varieties with h2,0=1. Duke Math J. 166 (2017), 739-799. Erratum
Ben Moonen and Qizheng Yin Some remarks on modified diagonals. Commun. Contemp. Math., published online November 2014. Final published version in Volume 18, issue 01, February 2016, 16 pages.
Ben Moonen On the Chow motive of an abelian scheme with non-trivial endomorphisms. Journal für reine und angewandte Mathematik, published online January 2014. Final published version in Volume 2016, issue 711, February 2016, pages 75-109.
Ben Moonen and Frans Oort The Torelli locus and special subvarieties. Handbook of Moduli (G. Farkas and I. Morrisson, eds.), Vol. 2, pp. 549-594. International Press, 2013.
Ben Moonen Special subvarieties arising from families of cyclic covers of the projective line. Documenta Math. 15 (2010), 793-819.
Ben Moonen and Alexander Polishchuk Divided powers in Chow rings and integral Fourier transforms. Advances in Math. 224 (2010), 2216-2236.
Ben Moonen and Alexander Polishchuk Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. II. J. de l'Institut Math. Jussieu 9 (2010), 799-846.
Bas Edixhoven, Gerard van der Geer and Ben Moonen (eds.) Modular forms on Schiermonnikoog, Cambridge Univ. Press, 2008.
Ben Moonen Relations between tautological cycles on Jacobians. Comm. Math. Helvetici 84 (2009), 471-502.
Gerard v.d. Geer, Ben Moonen and René Schoof (eds.) Number fields and function fields - two parallel worlds. Progress in Math. 239, Birkhäuser, 2005.
Ben Moonen Mod p period domains. Oberwolfach Reports 1 (2004), 1988-1991.
Ben Moonen and Torsten Wedhorn Discrete invariants of varieties in positive characteristic. IMRN 72 (2004), 3855-3903.
Ben Moonen Serre-Tate theory for moduli spaces of PEL-type. Ann. scient. de l'Ec. Norm. Sup. 37 (2004), 223-269.
Ben Moonen A dimension formula for Ekedahl-Oort strata. Ann. de l'Institut Fourier 54 (2004), 666-698.
Ben Moonen Group schemes with additional structures and Weyl group cosets. In: Moduli of abelian varieties (Texel Island, 1999), 255-298, Progress in Math. 195, Birkhäuser, 2001.
Bas Edixhoven, Ben Moonen and Frans Oort Open problems in algebraic geometry. Bull. Sci. Math. 125 (2001), 1-
Ben Moonen and Yuri Zarhin Hodge classes on abelian varieties of low dimension. Math. Ann. 315 (1999), 711-733.
Ben Moonen Models of Shimura varieties in mixed characteristics. In: Galois representations in arithmetic algebraic geometry (Durham, 1996), 267-350, LMS Lecture Note Ser. 254, Cambridge Univ. Press, 1998.
Yuri Zarhin and Ben Moonen

Weil classes and Rosati involutions on complex abelian varieties. In: Recent progress in algebra, 229-236, Contemp. Math. 224, AMS, 1999.

Ben Moonen Linearity properties of Shimura varieties. II. Compositio Math. 114 (1998), 3-35.
Ben Moonen Linearity properties of Shimura varieties. I. J. Algebraic Geom. 7 (1998), 539-567.
Ben Moonen Special points and linearity properties of Shimura varieties. PhD thesis, Univ. of Utrecht, 1995.
Ben Moonen and Yuri Zarhin Weil classes on abelian varieties. J. Reine Angew. Math. 496 (1998), 83-92.
Ben Moonen and Yuri Zarhin Hodge classes and Tate classes on simple abelian fourfolds. Duke Math. J. 77 (1995), 553-581.
Ben Moonen The Picard number of certain algebraic surfaces. J. Pure Appl. Algebra 85 (1993), 317-330.

Lecture notes

Topologie. (In Dutch) Syllabus voor een tweedejaars inleidend vak in de topologie.

Introduction to Algebraic Geometry. Notes based on a Mastermath course in the Spring of 2013.

Notes on Mumford-Tate groups. In 1999 I gave a series of lectures at the Centre Emile Borel in Paris about Mumford-Tate groups and images of Galois representations. The notes that I wrote are not widely available, and the notes of the second half of the course only exist in handwritten form. Should I one day find the time for it, I will write up a better and more complete set of notes. For the time being, I simply post the original notes of the first part of the course, even though the result is far from perfect. Comments are welcome!

There is another set of notes, corresponding to lectures I gave at a workshop in Monte Verita in 2004. Like the previous set, they should one day become part of a more complete text. For now, here are the original: An introduction to Mumford-Tate groups.

Draft for a book on abelian varieties

Jointly with Gerard van der Geer and Bas Edixhoven, I'm working on a book on Abelian Varieties. Unfortunately, the project has been dormant for a while, but I hope we shall be able to continue in the near future. Meanwhile, I here post the chapters that are currently available in preliminary form.

Front matter Title page and preliminaries
Chapter 1 Definition and basic examples
Chapter 2 Line bundles and divisors on abelian varieties
Chapter 3 Basic theory of group schemes
Chapter 4 Quotients by group schemes
Chapter 5 Isogenies
Chapter 6 The Picard scheme of an abelian variety
Chapter 7 Duality
Chapter 8 The theta group of a line bundle
Chapter 9 The cohomology of line bundles
Chapter 10 Tate modules, p-divisible groups, and the fundamental group
Chapter 11 Polarizations and the Weil pairing
Chapter 13 The Fourier transform and the Chow ring
Chapter 12 Endomorphims (very preliminary version)
Back matter References