Lie Fu and Ben Moonen | The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic p ≥ 5. Preprint, 2022 (50 pp). You can also download the Magma files as a zipped folder, with output and some documentation. |
Lie Fu and Ben Moonen | Algebraic cycles on Gushel-Mukai varieties. Preprint, 2022 (24 pp). To appear in EPIGA (Épijournal de Géométrie Algébrique), special issue in honour of Claire Voisin. |
Ben Moonen | The Coleman-Oort Conjecture: reduction to three key cases. Bulletin of the LMS, 2022 (Open Access). |
Ben Moonen | Computing discrete invariants of varieties in positive characteristic, I. Ekedahl-Oort types of curves. Journal of Pure and Applied Algebra, 2022 (Open Access). There is a Magma implementation available. In Section 4 of the paper it is described how this works. |
Ben Moonen | A remark on the Tate conjecture. J. of Algebraic Geometry 28 (2019), no. 3, 599-603. |
Ben Moonen | Families of Motives and the Mumford-Tate Conjecture. Milan J. of Math. 85 (2017), 257-307. Here is an Erratum and Addendum. |
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. J. of the Institute of Math. of Jussieu, 2018. |
Ben Moonen | On the Tate and Mumford-Tate conjectures in codimension one for varieties with h^{2,0}=1. Duke Math J. 166 (2017), 739-799. Here is an Erratum, and here is an Addendum. |
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. Here are some errata and an example. |
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. Corrigendum. |
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. Here is an Erratum. |
Ben Moonen and Yuri Zarhin | Weil classes on abelian varieties. J. Reine Angew. Math. 496 (1998), 83-92. Erratum. |
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. |
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.
I'm no longer involved in the book project on abelian varieties. I here post some chapters in preliminary form. Contact Gerard van der Geer if you have questions about this.
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 12 | Endomorphims (very preliminary version) |
Back matter | References |
Ben Moonen | Fieldsmedaille voor Peter Scholze. Nieuw Archief voor de Wiskunde 5/20, nr. 1, maart 2019. |