Departement Mathematik

Number theory seminar

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Herbstsemester 2016

Datum / Zeit Referent:in Titel Ort
14. Oktober 2016
14:15-15:15 		Dr. Robert Kucharczyk
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Absolute Galois groups and rational Witt vectors
Referent:in, Affiliation Dr. Robert Kucharczyk, ETH Zurich, Switzerland
Datum, Zeit 14. Oktober 2016, 14:15-15:15
Ort HG G 43
Abstract In this talk I will present a construction that, for each field containing the maximal cyclotomic extension of the rationals, realises the absolute Galois group of this field as the profinite fundamental group of an infinite-dimensional compact Hausdorff space, and also as the étale fundamental group of a scheme over the complex numbers. In a certain sense these spaces serve as classifying spaces for the absolute Galois group. We can also determine their classical fundamental groups (defined in terms of loops) and construct closely related spaces where we can partially make sense of descent along the cyclotomic extension. This is joint work with Peter Scholze (Bonn).
Absolute Galois groups and rational Witt vectorsread_more
HG G 43
* 19. Oktober 2016
14:00-15:00 		Chia-Fu Yu
Academica Sinica and MPI Bonn
Details

Number Theory Seminar

Titel On non-emptiness of Newton strata of Shimura varieties
Referent:in, Affiliation Chia-Fu Yu, Academica Sinica and MPI Bonn
Datum, Zeit 19. Oktober 2016, 14:00-15:00
Ort HG G 19.1
On non-emptiness of Newton strata of Shimura varieties
HG G 19.1
21. Oktober 2016
14:15-15:15 		Chia-Fu Yu
Academica Sinica and MPI Bonn
Details

Number Theory Seminar

Titel On endomorphism algebras of abelian varieties
Referent:in, Affiliation Chia-Fu Yu, Academica Sinica and MPI Bonn
Datum, Zeit 21. Oktober 2016, 14:15-15:15
Ort HG G 43
On endomorphism algebras of abelian varieties
HG G 43
28. Oktober 2016
14:15-15:15 		Dr. Maxim Mornev
University of Amsterdam
Details

Number Theory Seminar

Titel Shtuka cohomology and special values of Drinfeld modules
Referent:in, Affiliation Dr. Maxim Mornev, University of Amsterdam
Datum, Zeit 28. Oktober 2016, 14:15-15:15
Ort HG G 43
Abstract The motivic Tamagawa number conjecture expresses the special values of L-functions in terms of motivic cohomology. Among other things it integrates the analytic class number formula for number fields, and the BSD conjecture in a single framework. While this conjecture is exceptionally hard, it has a tractable analogue in positive characteristic as discovered by Lenny Taelman. Here the usual L-functions are replaced by Goss L-functions which take values in a positive characteristic field, and one is interested in Goss L-functions attached to Drinfeld modules. In the talk I will explain how the special values of these L-functions can be expressed in terms of shtuka cohomology which plays the role of motivic cohomology in this story.
Shtuka cohomology and special values of Drinfeld modulesread_more
HG G 43
11. November 2016
14:15-15:15 		Dr. Netan Dogra
Imperial College London
Details

Number Theory Seminar

Titel An explicit Chabauty-Kim Theorem
Referent:in, Affiliation Dr. Netan Dogra, Imperial College London
Datum, Zeit 11. November 2016, 14:15-15:15
Ort HG G 43
Abstract In 1938, Chabauty proved the Mordell conjecture in the special case when the Mordell-Weil rank of the Jacobian is less than the genus. Chabauty's method produces a finite set of p-adic points which contains the rational points, and can often be computed in practice. Later, Coleman re-interpreted Chabauty's method and proved an explicit bound on the size of this "Chabauty set", and hence on the number of rational points. Recently, Kim has suggested a nonabelian generalisation of Chabauty's method, which produces finite sets of p-adic points containing the rational points under weaker hypotheses on the underlying curve. In this talk we describe work in progress with Jennifer Balakrishnan on a nonabelian generalisation of Coleman's theorem, providing a bound on the size of the "Chabauty-Kim sets" that arise in Kim's theory.
An explicit Chabauty-Kim Theoremread_more
HG G 43
* 16. November 2016
14:00-15:00 		Prof. Dr. Umberto Zannier
Scuola Normale Superiore di Pisa
Details

Number Theory Seminar

Titel On the Hilbert Property and the fundamental group of algebraic varieties
Referent:in, Affiliation Prof. Dr. Umberto Zannier, Scuola Normale Superiore di Pisa
Datum, Zeit 16. November 2016, 14:00-15:00
Ort HG G 19.1
On the Hilbert Property and the fundamental group of algebraic varieties
HG G 19.1
25. November 2016
14:15-15:15 		Dr. Hadi Hedayatzadeh
IPM Tehran and FIM
Details

Number Theory Seminar

Titel The wedge morphism on the Lubin-Tate space
Referent:in, Affiliation Dr. Hadi Hedayatzadeh, IPM Tehran and FIM
Datum, Zeit 25. November 2016, 14:15-15:15
Ort HG G 43
Abstract p-divisible groups are smooth formal group schemes which naturally arise as injective limits of p-power torsion in algebraic groups. A celebrated theorem of Serre and Tate states that the deformation theory of an abelian variety over perfect fields is equivalent to the deformation theory of its p-divisible group, and so there is a deep connection between modular forms, which live in the cohomology of moduli spaces of abelian varieties (Shimura varieties) and deformations of p-divisible groups (Lubin-Tate and Rapoport-Zink spaces). These deformation spaces appear naturally in the Langlands program. Indeed, the local Langlands correspondence for GL_n is realized in the cohomology of Lubin-Tate space. Also, Kottwitz’ conjecture posits that certain cases of local Langlands correspondence (for more general reductive groups) are realized in the cohomology of Rapoport-Zink spaces and whether they contain any supercuspidal representations. In this talk, I will talk about p-divisible groups and their deformation spaces. I will then discuss the existence of exterior powers of p-divisible groups and explain how their construction defines a natural map between certain deformation (Rapoport-Zink) spaces. This would imply the existence, e.g., of a determinant map between deformation spaces of p-divisible groups, with implications for recent work of Scholze and Weinstein. If time permits, I will also talk about the applications to the study of certain supercuspidal representations appearing in the cohomology of Rapoport-Zink spaces.
The wedge morphism on the Lubin-Tate spaceread_more
HG G 43
2. Dezember 2016
14:15-15:15 		Yunqing Tang
Institute for Advanced Study
Details

Number Theory Seminar

Titel Cycles in the de Rham cohomology of abelian varieties over number fields
Referent:in, Affiliation Yunqing Tang, Institute for Advanced Study
Datum, Zeit 2. Dezember 2016, 14:15-15:15
Ort HG G 43
Abstract In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus and Blasius. Ogus predicted that all such cycles are Hodge. In this talk, I will first introduce Ogus’ conjecture as a crystalline analogue of Mumford–Tate conjecture and explain how a theorem of Bost (using methods a la Chudnovsky) on algebraic foliation is related. After this, I will discuss the proof of Ogus’ conjecture for some families of abelian varieties under the assumption that the cycles lie in the Betti cohomology with real coefficients.
Cycles in the de Rham cohomology of abelian varieties over number fieldsread_more
HG G 43
9. Dezember 2016
14:15-15:15 		Prof. Dr. Bora Yalkinoglu
Université de Strasbourg
Details

Number Theory Seminar

Titel On Complex Multiplication and higher Teichmüller theory
Referent:in, Affiliation Prof. Dr. Bora Yalkinoglu, Université de Strasbourg
Datum, Zeit 9. Dezember 2016, 14:15-15:15
Ort HG G 43
Abstract An ingenious calculation of T. Shintani forty years ago demonstrated that abelian extensions of imaginary quadratic number fields can be expressed in terms of special values of a two-dimensional Gamma function (and he famously conjectured that the same should hold for real quadratic number fields). The goal of this talk will be to outline a strategy to understand the calculation of Shintani in a geometric manner. The main protagonists in this story are the higher Teichmüller spaces (or more generally cluster varieties) introduced by V. Fock and A. Goncharov.
On Complex Multiplication and higher Teichmüller theoryread_more
HG G 43
16. Dezember 2016
14:15-15:15 		Dr. Oliver Bültel
Universität Essen
Details

Number Theory Seminar

Titel $(G,\mu)$-displays and Rapoport-Zink spaces
Referent:in, Affiliation Dr. Oliver Bültel, Universität Essen
Datum, Zeit 16. Dezember 2016, 14:15-15:15
Ort HG G 43
Abstract Let $(G,\mu)$ be a pair of a reductive group $G$ over the $p$-adic integers and a minuscule cocharacter $\mu$ of $G$ defined over an unramified extension. We introduce the notion of "$(G,\mu)$-display" which generalizes Zink's Witt vector displays. We use these to define Rapoport-Zink formal schemes purely group theoretically, i.e. without using $p$-divisible groups. This is joint work with G. Pappas.
$(G,\mu)$-displays and Rapoport-Zink spacesread_more
HG G 43

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

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