The Bielefeld Arithmetic Geometry Seminar 2014 (summer term)

Welcome to the website of the 3rd edition of the Bielefeld arithmetic geometry seminar! Below you will find a list of the upcoming talks, hover with your mouse over abstract to see the abstract. The seminar is related to projects B5 and C7.
The seminar is supported by the SFB CRC 701: Spectral Structures and Topological Methods in Mathematics.

Talks

Wednesday April 30, 2014
16:00	X-E0-230	Tobias Schmidt (University of Muenster) Arithmetic D-modules and locally analytic representations [Abstract] The classical theorem of Beilinson-Bernstein describes representations of a complex semisimple Lie algebra via differential equations on its flag manifold. In this talk I will explain how an arithmetic version of this result can be used to study locally analytic representations of p-adic Lie groups. This is joint work with C. Noot-Huyghe.
Wednesday May 14, 2014
16:00	X-E0-230	Grzegorz Banaszak (Adam Mickiewicz University) The algebraic Sato-Tate group and Sato-Tate conjecture [Abstract] Let $K$ be a number field, and let $A$ be an abelian variety over $K$. In order to find the proper setting of the Sato-Tate conjecture concerning the equidistribution of Frobenius elements in the representation of the Galois group of $K$ on the Tate module of $A$, one of the attempts is the introduction of the algebraic Sato-Tate group $AST_K(A)$. Maximal compact subgroups of $AST_K(A)({\mathbb C})$ are expected to be the key tool for the statement of the Sato-Tate conjecture for $A$. Following an idea of J-P. Serre, the explicit construction of $AST_K(A)$ will be presented based on P. Deligne's motivic category of absolute Hodge cycles and the corresponding motivic Galois group. I will also discuss the arithmetic properties of $AST_K(A)$ along with explicit computations of $AST_K(A)$ for some families of abelian varieties. This construction of the algebraic Sato-Tate group can be done more generally than for abelian varieties, it can also be done for absolute Hodge cycle motives. This is joint work with Kiran Kedlaya.
Wednesday May 28, 2014
16:00	X-E0-230	Nirinjan Ramachandran (University of Maryland) The de Rham Witt complex and special values of zeta functions [Abstract] The special values of zeta functions of varieties over finite fields can be described (conjecturally) as Euler characteristics via $\ell$-adic cohomology or Weil-etale cohomology. This description is up to powers of the characteristic of the finite field. The $p$-part of the special value can be described using de Rham Witt cohomology. This talk will begin with a review of the classical conjectures on special values and then sketch some recent results obtained jointly with J. Milne.
Wednesday July 2, 2014
16:00	X-E0-230	Ulrich Derenthal (University of Hannover) Cox rings and rational points on cubic surfaces [Abstract] For cubic surfaces over number fields, the distribution of rational points is predicted by Manin's conjecture. This has been extensively studied over the field Q of rational numbers using universal torsors and Cox rings. In this talk, I will give an introduction to this subject and discuss how this method can be generalized to other number fields.
Wednesday July 9, 2014
16:00	X-E0-230	Giovanni Rosso Trivial zero for the symmetric square of an elliptic curve over a totally real field [Abstract] Let $p$ be a prime, in the 90's Greenberg formulated a very nice conjecture concerning the values of the derivative of the $p$-adic $L$-function of a motive $M$ when the so-called trivial zeros appear. The aim of the talk is to present in detail this conjecture and to give a proof of it in the particular case of the symmetric square of a modular elliptic curve $E$ over a totally field $F$, when $p$ is inert in $F$ and $E$ has multiplicative reduction at $p$ (plus some other small hypothesis on the conductor). This work is a generalization of (unpublished) work of Greenberg and Tilouine.
Thursday July 17, 2014
10:00	X-E0-214	Eike Lau (University of Paderborn) Crystalline Dieudonne theory via generalised Dieudonne displays [Abstract] We study the crystalline Dieudonne functor from the category of $p$-divisible groups to the category of Dieudonne crystals. It is known that the functor is an equivalence if the base is smooth, and that it is fully faithful if the base is a locally complete intersection. We determine the image of the functor over an l.c.i. base using a generalisation of Dieudonne displays.
11:00	X-E0-214	Andreas Langer (University of Exeter) Grothendieck-Messing deformation theory for Hyperkaehler varieties [Abstract] For an artinian ring $R$ with perfect residue field we define higher displays over the small Witt ring. In analogy to $p$-divisible groups we prove a result of Grothendieck-Messing type for hyperkaehler varieties: If $X$ is a Hyperkaehler variety over $R$ (for example a K3-surface) then deformations of $X$ over a nilpotent pd-thickening correspond uniquely to deformations of the associated $2$-display resp. its Hodge-filtration. For the proof we give an algebraic definition of the Beauville-Bogomolov-Form on the second de Rham cohomology of $X$ and show that for ordinary Hyperkaehler varieties the associated F-crystal is self-dual under the BB-pairing. This is joint work with Thomas Zink.

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Seminars

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The Bielefeld Arithmetic Geometry Seminar 2014 (summer term)

Talks

Wednesday

April 30, 2014

Wednesday

May 14, 2014

Wednesday

May 28, 2014

Wednesday

July 2, 2014

Wednesday

July 9, 2014

Thursday

July 17, 2014