The Bielefeld Arithmetic Geometry Seminar 2015 (summer term)

Welcome to the website of the 5th 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 8 April, 2015
16:15	X-E0-220	Jeanine van Order (MPI Bonn) $GL(n)$-automorphic $L$-functions in cyclotomic towers [Abstract] Let $\pi$ be a cuspidal automorphic representation of $GL(n)$ over a number field $F$. Let $p$ be a rational prime, and let $X$ be the set of all finite-order Hecke characters of $F$ obtained by composition with the norm homomorphism from $F$ to $\mathbb{Q}$ with some Dirichlet character of $p$-power conductor. In this talk, I will explain why one expects (and sometimes knows) that if $\pi$ is cohomological, then for all but finitely many characters $\xi$ in the set $X$, the central value $L(1/2, \pi \times \xi)$ does not vanish. Some preliminary results in this direction will also be presented.
Wednesday 22 April, 2015
16:15	X-E0-220	Aprameyo Pal (Duisburg-Essen) Algebraic functional equation of dual Selmer groups and duality [Abstract] Let $X$ be a Pontryagin dual of a Selmer group defined over a $p$-adic Lie extension. I will explain the algebraic functional equation relating $X$ with $X^{\sharp}$ (defined via action of the involution) in different setup. In general this gives some evidence towards Main conjectures of Iwasawa theory. On the other hand there is a purely algebraic interest in it (duality results). If time permits, I will explain some consequences of functional equations including parity results and growth of Selmer groups.
Wednesday 6 May, 2015
16:15	X-E0-220	Steffen Müller - Cancelled! (Oldenburg) Quadratic Chabauty [Abstract] I will introduce a method to $p$-adically approximate integral points on a hyperelliptic curve defined over the rationals whose genus is equal to the Mordell-Weil rank of its Jacobian. The method relies on $p$-adic heights and iterated Coleman integrals. If time permits, I will also discuss how this approach can be used to provably find all integral points and how it can be extended to curves defined over number fields. This is joint work with Jennifer Balakrishnan and Amnon Besser.
Wednesday 20 May, 2015
16:15	X-E0-220	Alessandro Cobbe (LMU Munich) Equivariant epsilon constant conjectures for weakly ramified extensions [Abstract] We study the local epsilon constant conjecture as formulated by Breuning. This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected compatibility of the ETNC with the functional equation of Artin-$L$-functions. Let $K/\mathbb Q_p$ be unramified. Under some mild technical assumption we prove Breuning's conjecture for weakly ramified abelian extensions $N/K$ with cyclic ramification group. As a consequence of Breuning's local-global principle we obtain the validity of the global epsilon constant conjecture as formulated by Bley and Burns and of Chinburg's $\Omega(2)$-conjecture for certain infinite families $F/E$ of weakly and wildly ramified extensions of number fields. This is a joint work with Werner Bley.
Wednesday 17 June, 2015
16:15	X-E0-220	Rodolfo Venerucci (Duisburg-Essen) Exceptional zero formulae and a conjecture of Perrin-Riou [Abstract] I will discuss $p$-adic analogues of the Birch and Swinnerton-Dyer conjecture for elliptic curves defined over the rationals, focusing on the exceptional-zero situation according to Mazur-Tate-Teitelbaum. In particular, I will outline a proof of the $p$-adic Gross-Zagier formula in this setting, grounded on Hida theory of $p$-adic families of modular forms. As a crucial step in the proof, we relate Beilinson-Kato elements to Heegner points, establishing a conjecture of Perrin-Riou.
Wednesday 1 July, 2015
16:15	X-E0-220	Arno Kret (MPI Bonn) Galois representations for the general symplectic group [Abstract] We explain how to construct Galois representations attached to automorphic representations of the general symplectic group over a totally real number field, under local simplifying hypotheses. This is joint work with Sug Woo Shin.
Friday 18 September, 2015
15:00	V3-201	Debargha Banerjee (Pune) Eisenstein elements inside the space of modular symbols [Abstract] The Eisenstein elements inside the space of modular symbols are the explicit elements of the space of modular symbols corresponding to Eisenstein series of weight two. In the talk, we will show how to write down an explicit rational expression of Eisenstein elements in terms of Manin symbols. We also compute the winding elements explicitly for some congruence subgroups. Our results are explicit versions of the Manin-Drinfeld Theorem. At the end, we will talk about a different way of writing down the Eisenstein elements using Hecke operators. This is joint with Loic Merel (University of Paris).

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Seminars

Conference

The Bielefeld Arithmetic Geometry Seminar 2015 (summer term)

Talks

Wednesday

8 April, 2015

Wednesday

22 April, 2015

Wednesday

6 May, 2015

Wednesday

20 May, 2015

Wednesday

17 June, 2015

Wednesday

1 July, 2015

Friday

18 September, 2015