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Algebraic and Arithmetic Geometry @ Bielefeld

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The Bielefeld Algebraic and Arithmetic Geometry Seminar 2019-2020

Welcome to the website of the Bielefeld Algebraic and Arithmetic Geometry Seminar! For more information, please contact the organizers: Eike Lau, Michael Spiess, Jeanine Van Order, Charles Vial, and Thomas Zink.

Talks

Thursday 29 August, 2019
14:00	V2-200	Igor Burban (Paderborn) Morita theorem for non-commutative schemes [Abstract]
Wednesday 9 October, 2019
15:30	V2-210	Johannes Anschütz (Bonn) Prismatic Dieudonne theory [Abstract] With the prismatic site of a p-complete ring Bhatt and Scholze introduced a mixed-characteristic analog of the crystalline site. Using this site we will present the definition of a prismatic Dieudonne functor which, in the interesting class of mod p quasi-syntomic rings, generalizes the classical crystalline Dieudonne functor of Berthelot/Breen/Messing. We will then sketch our main classification result for p-divisibe groups over quasi-syntomic rings and explain how to recover results of Breuil/Kisin/Lau for regular rings of mixed-characteristic.
17:00	V2-210	Eugenia Rosu, (MPIM-Bonn) Special cycles on orthogonal Shimura varieties [Abstract] Extending on the work of Kudla-Millson and Yuan-Zhang-Zhang, together with Yott we are constructing special cycles for a specific GSpin Shimura variety. We further construct a generating series that has as coefficients the cohomology classes corresponding to the special cycle classes on the GSpin Shimura variety and show the modularity of the generating series in the cohomology group over C.
Wednesday 30 October, 2019
15:30	V2-210	Matthias Schütt (Hannover) (Few) rational curves on K3 surfaces [Abstract] Rational curves play a fundamental role for the structure of a K3 surface. I will first review the general theory before focussing on the case of low degree curves where joint work with S. Rams (Krakow) extends bounds of Miyaoka and Degtyarev. Time permitting, I will also cover the special case of smooth rational curves.
17:00	V2-210	David Hansen, (MPIM-Bonn) Geometric Eisenstein series and the Fargues-Fontaine curve [Abstract] In the geometric Langlands program, one replaces automorphic forms on a group G with sheaves on the stack of G-bundles over a fixed projective curve. The analogue of Eisenstein series in this setting is the "Eisenstein functor" constructed 20 years ago by Braverman-Gaitsgory, which has many marvelous properties. Recently, Fargues has proposed a completely new kind of geometric Langlands program over the Fargues-Fontaine curve. I'll discuss the prospects for constructing an Eisenstein functor in this setting, and explain an application to the local Langlands correspondence. This is joint work in progress with Linus Hamann.
Wednesday 27 November, 2019
16:00	V2-210	Daniel Huybrechts (Bonn) Complex multiplication and twistor spaces [Abstract] Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarized K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.