CRC 326 - GAUS

Critical values of Hecke L-funktions
2025-06-12 14:15 - 15:15 (Europe/Berlin) | Mainz, Hilbertraum (05-432)
Han-Ung Kufner (Universität Regensburg)
A conjecture of Deligne from 1977 relates the critical values of a motivic
L-function with certain periods of the motive. The goal of this talk is to
explain Deligne’s conjecture and to discuss a proof in the case of Hecke
L-functions. This generalizes a result of Blasius for Hecke characters of CMfields.
For the proof we use the recently constructed Eisenstein-Kronecker
classes of Kings-Sprang and combine them with ideas from Blasius’ proof.
1

Berkovich motives
2025-06-12 15:00 - 16:30
Talk 8: K-theory (Christian Dahlhausen)

Quantitative level lowering for modular forms
2025-06-13 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Quantitative level lowering for modular forms
Mohamed Moakher (University of Pittsburgh)
Given a Hilbert modular form f of weight two over a totally real field F, we can associate to it a finite module Phi(f) known as the congruence module for f, which measures the congruences that f satisfies with other forms. When f is transferred to a quaternionic modular form f_D over a quaternion algebra D via the Jacquet-Langlands correspondence, we can similarly define a congruence module Phi(f_D) for f_D. Pollack and Weston proposed a quantitative relationship between the sizes of Phi(f) and Phi(f_D), expressed in terms of invariants associated to f and D. In this talk, I will outline the ideas underlying the proof of this relationship. The approach combines a method of Ribet and Takahashi with new techniques introduced by Böckle, Khare, and Manning.

Seminar on Arithmetic Geometry
2025-06-13 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Emanuel Reinecke (IHES): Poincare duality for proper morphisms in rigid geometry
While the Z/p-etale cohomology of rigid-analytic varieties is in general hard to control, it becomes more tractable when the varieties are proper. In my talk, I will explain a relative Poincare duality statement for etale cohomology with finite coefficients which applies to any proper morphism of rigid-analytic varieties over nonarchimedean fields of mixed characteristic, confirming an expectation of Bhatt-Hansen. A key ingredient in the proof will be a construction of trace maps for proper morphisms. Joint work with Shizhang Li and Bogdan Zavyalov.
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Conference "Étale cohomology and étale homotopy"
2025-06-16 - 2025-06-20 | Frankfurt am Main

Motivic Spectra
2025-06-16 10:15 - 11:45 | Mainz, Hilbertraum (05-432) and Zoom
Talk 6: Snaith Theorem for algebraic K-theory (Lorenzo Mantovani)

Categorical Deligne–Langlands correspondence
2025-06-17 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Jon Miles: Talk 8 – The Kazhdan–Lusztig classification
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Seminar on Arithmetic Geometry
2025-06-20 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Thiago Landim (IMJ): Weights and motives on stacks
The existence of a motivic t-structure is an old problem in the center of many conjectures related with algebraic cycles. Inspired by Deligne, Bondarko defined a dual notion, now called weight structure, and proved Beilinson motives (and later integral cdh-motives) on nice schemes admit weight structures. In this talks, we are going to prove the category of K-motives (modules of genuine K-theory inside motivic spectra) on tame quotient stacks, as defined by Hoyois, admits a well-behaved category of geometric motives and prove the existence of bounded weight structure on them. If time allows, we are going to explain how this behaves better for Kan extended theories, e.g. cdh-motives, and how étale sheaves behaves even better.
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Categorical Deligne–Langlands correspondence
2025-06-24 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 10 – Interpolation in families
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Locally analytic vector bundles on the Fargues-Fontaine-Curve - Copy
2025-06-26 11:15 - 13:15 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Acyclicity of locally analytic vectors
speaker: Marvin Schneider (Heidelberg)

Berkovich motives
2025-06-26 13:00 - 14:30
Talk 9: Dmot(X) (Chirantan Chowdhury)

Anabelian geometry - Daniel Litt "Arithmetic representations of fundamental groups II"
2025-06-26 14:00 - 17:30 | Heidelberg
14:00 – 15:15
15:45 – 17:00

D-elliptic sheaves and the Hasse principle
2025-06-27 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
p-adic properties
Alireza Shavali (Heidelberg)

Bogomolov property for Galois representations with big local image
2025-06-27 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Andrea Conti (Heidelberg)
An algebraic extension of the rational numbers is said to have the Bogomolov property if the absolute logarithmic Weil height of its non-torsion elements is uniformly bounded from below. Given a continuous representation $rho$ of the absolute Galois group $G_{mathbb Q}$ of $mathbb Q$, one can ask whether the field fixed by $mathrm{ker}(rho)$ has the Bogomolov property (in short, we say that $rho$ has (B)). In a joint work with Lea Terracini, we prove that, if $rhocolon G_{mathbb Q}tomathrm{GL}_N(mathbb Z_p)$ maps an inertia subgroup at $p$ surjectively onto an open subgroup of $mathrm{GL}_N(mathbb Z_p)$, then $rho$ has (B). More generally, we show that if the image of a decomposition group at $p$ is open in the image of $G_Q$, plus a certain condition on the center of the image is satisfied, then $rho$ has (B). In particular, no assumption on the modularity of $rho$ is needed, contrary to previous work of Habegger and Amoroso—Terracini.

Seminar on Arithmetic Geometry
2025-06-27 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Tianyi Feng (University Bonn): Metaplectic Satake with Ring Coefficients
In this talk we explain the statement and proof strategy of the geometric Satake equivalence for topological (aka metaplectic) coverings of reductive groups in DVR coefficients. This is joint work in progress with Yifei Zhao.
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Motivic Spectra
2025-06-30 10:15 - 11:45 | Mainz, Hilbertraum (05-432) and Zoom
Talk 7: Algebraic Cobordism (Julie Bannwart)

Motivic Spectra
2025-06-30 10:15 - 11:45 | Mainz, Hilbertraum (05-432) and Zoom
Talk 9: Snaith Theorem for periodic algebraic cobordism (Anton Engelmann)

Categorical Deligne–Langlands correspondence
2025-07-01 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 11 – Main conjecture in the regular case
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Equivariant aspects of Hochschild homology
2025-07-03 09:00 - 10:00 | Mainz, Poissonraum (04-220), Staudingerweg 9, Rheinland-Pfalz - Mainz, 55128, Germany
Zhouhang Mao (University of Amsterdam)
Abstract: Many localizing invariants, after being applied to schemes, are equipped with a motivic filtration whose associated graded pieces are given by cohomology theories of schemes. In this talk, we give an equivariant aspects of two localizing invariants proposed by Kaledin, which correspond to non-Hodge-completed derived de Rham cohomology and de Rham–Witt complex respectively. Our description adapts to prismatic cohomology as well. If time permits, we also give an unexpected application of these considerations to prismatic logarithm.

Locally analytic vector bundles on the Fargues-Fontaine-Curve
2025-07-03 11:15 - 13:15 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Descent to locally analytic vectors
Max Witzelsperger (Heidelberg)

D-elliptic sheaves and the Hasse principle
2025-07-04 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Determinants of D-elliptic sheaves
speaker Giacomo Hermes Ferraro (Heidelberg)

Algebraic K-theory and the universal localising invariant
2025-07-04 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Algebraic K-theory and the universal localising invariant
Christoph Winges (Universität Regensburg)
Essentially by construction, the abelian group K_0 is the target of the universal rank function for various types of objects, including finitely generated projective modules and perfect chain complexes. Over the last couple of decades, it has become possible to formulate and prove a similar universal property for higher algebraic K-theory in the sense of Quillen and Waldhausen. A closer inspection of various localisation phenomena in algebraic K-theory leads to the notion of a localising invariant, among which algebraic K-theory enjoys a similar universal property due to work of Blumberg, Gepner and Tabuada. I will survey these results and, as time allows, discuss an alternative perspective on parts of this story that I obtained in recent joint work with Ramzi and Sosnilo.

Seminar on Arithmetic Geometry
2025-07-04 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Matteo Tamiozzo (Université Sorbonne Paris Nord): Towards semi-global plectic conjectures
Known results on the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank at most one over totally real fields rely on CM points on Shimura curves. After recalling this, I will illustrate how an attempt to go beyond rank one leads to the plectic conjectures of Nekovář-Scholl for higher-dimensional quaternionic Shimura varieties. Finally, I will present joint work in progress with Tony Feng and Mingjia Zhang aimed at proving a “semi-global” version of these conjectures.
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Conference: Geometry and Representation Theory around the Langlands programs
2025-07-07 - 2025-07-11 | Clermont-Ferrand, France

Motivic Spectra
2025-07-07 10:15 - 11:45 | Mainz, Hilbertraum (05-432) and Zoom
Talk 8: Algebraic Conner-Floyd isomorphism (Philipp Schleiß)

Categorical Deligne–Langlands correspondence
2025-07-08 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Torsten Wedhorn: Talk 12 – Proof of the main conjecture for GL2
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Berkovich motives
2025-07-10 11:00 - 12:30
Talk 10: Dmot(C) (Alberto Merici)

Locally analytic vector bundles on the Fargues-Fontaine-Curve
2025-07-10 11:15 - 13:15 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Locally analytic vector bundles and p-adic differential equations
Ruth Wild (Frankfurt)

Berkovich motives
2025-07-10 14:00 - 15:30
Talk 11: Dmot(k) (Can Yaylali)

D-elliptic sheaves and the Hasse principle
2025-07-11 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
The canonical isogeny character
speaker: Gebhard Böckle, Heidelberg
