HU Arithmetic Geometry Seminar

Humboldt Arithmetic Geometry Seminar

Humboldt University Berlin, Summer 2025

Time: Tuesdays 15:15 - 16:45

Venue: Room 3.006, Rudower Chaussee 25, 12489 Berlin

— See also the Algebraic Geometry Seminars at HU and FU —


NOTE:	This semester the seminar will take place from 15:15 - 16:45 !!!
20.05.2025	Marco Maculan (Jussieu, Paris)
Title:	Affine vs. Stein in rigid geometry
Abstract:	What is the relation between coherent cohomology on a complex variety and that of the associated analytic space? The natural map between them is certainly not surjective for cardinality reasons. It is not even injective in general: this is a consequence of the existence of a nonaffine algebraic variety which is Stein. In a joint work with J. Poineau, we show that over non-Archimedean field the situation is, pun intended, far more rigid.
10.06.2025	Abhishek Oswal (Freiburg)
Title:	p-adic hyperbolicity of the moduli space of abelian varieties
Abstract:	By a theorem of Borel, any holomorphic map from a complex algebraic variety to the moduli space of abelian varieties (and more generally to an arithmetic variety) is in fact algebraic. A key input is to prove that any holomorphic map from a product of punctured disks to such an arithmetic variety does not have any essential singularities. In this talk, I'll discuss a p-adic analogue of these results. This is joint work with Ananth Shankar and Xinwen Zhu (with an appendix by Anand Patel).
THURSDAY 19.06.2025	Philip Engel (Chicago, Illinois)
Title:	Boundedness theorems for abelian fibrations
Abstract:	I will report on forthcoming work, joint with Filipazzi, Greer, Mauri, and Svaldi, on boundedness results for abelian fibrations. We will discuss a proof that irreducible Calabi-Yau varieties admitting an abelian fibration are birationally bounded in a fixed dimension; and that Lagrangian fibrations of symplectic varieties, in a fixed dimension, are analytically bounded. Conditional on the generalized semiampleness/hyperkahler SYZ conjecture, this bounds the number of deformation classes of hyperkahler varieties in a fixed dimension, with second Betti number at least 5.
24.06.2025	Denis-Charles Cisinski (Regensburg)
Title:	tba
Abstract:	tba

NOTE:

This semester the seminar will take place from 15:15 - 16:45 !!!

20.05.2025

Marco Maculan (Jussieu, Paris)

Title:

Affine vs. Stein in rigid geometry

Abstract:

What is the relation between coherent cohomology on a complex variety and that of the associated analytic space? The natural map between them is certainly not surjective for cardinality reasons. It is not even injective in general: this is a consequence of the existence of a nonaffine algebraic variety which is Stein. In a joint work with J. Poineau, we show that over non-Archimedean field the situation is, pun intended, far more rigid.

10.06.2025

Abhishek Oswal (Freiburg)

Title:

p-adic hyperbolicity of the moduli space of abelian varieties

Abstract:

By a theorem of Borel, any holomorphic map from a complex algebraic variety to the moduli space of abelian varieties (and more generally to an arithmetic variety) is in fact algebraic. A key input is to prove that any holomorphic map from a product of punctured disks to such an arithmetic variety does not have any essential singularities. In this talk, I'll discuss a p-adic analogue of these results. This is joint work with Ananth Shankar and Xinwen Zhu (with an appendix by Anand Patel).

THURSDAY 19.06.2025

Philip Engel (Chicago, Illinois)

Title:

Boundedness theorems for abelian fibrations

Abstract:

I will report on forthcoming work, joint with Filipazzi, Greer, Mauri, and Svaldi, on boundedness results for abelian fibrations. We will discuss a proof that irreducible Calabi-Yau varieties admitting an abelian fibration are birationally bounded in a fixed dimension; and that Lagrangian fibrations of symplectic varieties, in a fixed dimension, are analytically bounded. Conditional on the generalized semiampleness/hyperkahler SYZ conjecture, this bounds the number of deformation classes of hyperkahler varieties in a fixed dimension, with second Betti number at least 5.

24.06.2025

Denis-Charles Cisinski (Regensburg)

Title:

tba

Abstract:

tba