Arithmetic & Homotopic Galois Theory IRN | Perverse sheaves and the Shafarevich conjecture

January 19, 2026	Perverse sheaves and the Shafarevich conjecture Thomas Krämer, TU Chemnitz, DE RIMS Kyoto (Room 110) + Zoom · JP: 16:30 · FR: 08:30 The Shafarevich conjecture, a special case of the Lang-Vojta conjecture in Diophantine geometry, predicts that over any number field there only finitely many isomorphism classes of smooth projective canonically polarized varieties with given Hilbert polynomial and good reduction outside a given finite set of primes. For curves this was famously proven by Faltings on his way to the Mordell conjecture, but the higher-dimensional case remains wide open. In the talk I will discuss joint work with Marco Maculan in which we prove the Shafarevich conjecture for a large class of varieties with globally generated cotangent bundle. We combine the Lawrence-Sawin-Venkatesh method with the big monodromy theorem from our work with Javanpeykar, Lehn and Maculan. The key input is the convolution of perverse sheaves on abelian varieties.
T. Krämer and M. Maculan, The Shafarevich conjecture for varieties with globally generated cotangent. Preprint (2025) [ArXiV] T. Krämer and M. Maculan, Arithmetic finiteness of very irregular varieties. Duke Math. J. (to appear). Preprint (2025) [ArXiV] A. Javanpeykar, T. Krämer, C. Lehn and M. Maculan, The monodromy of families of subvarieties on abelian varieties. Duke Math. J. 174 (2025), 1045-1149 [ArXiV].
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January 19, 2026

Perverse sheaves and the Shafarevich conjecture

Thomas Krämer, TU Chemnitz, DE RIMS Kyoto (Room 110) + Zoom · JP: 16:30 · FR: 08:30

The Shafarevich conjecture, a special case of the Lang-Vojta conjecture in Diophantine geometry, predicts that over any number field there only finitely many isomorphism classes of smooth projective canonically polarized varieties with given Hilbert polynomial and good reduction outside a given finite set of primes. For curves this was famously proven by Faltings on his way to the Mordell conjecture, but the higher-dimensional case remains wide open.

In the talk I will discuss joint work with Marco Maculan in which we prove the Shafarevich conjecture for a large class of varieties with globally generated cotangent bundle. We combine the Lawrence-Sawin-Venkatesh method with the big monodromy theorem from our work with Javanpeykar, Lehn and Maculan. The key input is the convolution of perverse sheaves on abelian varieties.

T. Krämer and M. Maculan, The Shafarevich conjecture for varieties with globally generated cotangent. Preprint (2025) [ArXiV]
T. Krämer and M. Maculan, Arithmetic finiteness of very irregular varieties. Duke Math. J. (to appear). Preprint (2025) [ArXiV]
A. Javanpeykar, T. Krämer, C. Lehn and M. Maculan, The monodromy of families of subvarieties on abelian varieties. Duke Math. J. 174 (2025), 1045-1149 [ArXiV].