[Turkmath:652] Re: Workshop on Iwasawa theory and (p-adic) Beilinson conjectures

[Kazım Büyükboduk]

Dear Colleagues,

Following up on my previous announcement, here I attach (as a PDF file) the
poster for the workshop on "IWASAWA THEORY AND (P-ADIC) BEILINSON
CONJECTURES" with the program.

Please consult below for the abstracts of the talks.

We once again thank IMBM for hosting this workshop.

Kazim Buyukboduk


On Mon, Sep 7, 2015 at 8:35 AM, Kazım Büyükboduk <kbuyukboduk at ku.edu.tr>
wrote:

> Dear All,
>
> IMBM (Bogazici University, Istanbul) will host our workshop on "Iwasawa
> theory and (p-adic) Beilinson conjectures" to take place on September 15th
> (Tuesday) and September 17th (Thursday). Please find the program of the
> talks and the abstracts at the bottom of this e-mail message.
>
> We express our deep gratitude to IMBM for generously hosting the two
> speakers (Masataka Chida visiting from Tohoku and Fabien Trihan from
> Tokyo). The talks will take place in the IMBM building (located in the
> Bogazici University South Campus). We welcome all interested audience!
>
> Kazim Buyukboduk
>
>
> WORKSHOP ON IWASAWA THEORY AND (P-ADIC) BEILINSON CONJECTURES
>
> PROGRAM:
>
> September 15th, Tuesday:
>
> 10:30-12:00: Fabien Trihan (Tokyo)
> Geometric Iwasawa Main and Equivariant Tamagawa Number Conjectures - I
>
> 13:30-14:30: Kazim Buyukboduk
> Exceptional zeros of p-non-ordinary forms and Perrin-Riou's conjecture - I
>
> 15:00-16:30: Masataka Chida (Tohoku)
> Selmer groups and the central values of L-functions for modular forms.
>
>
> September 17th, Thursday:
>
> 10:30-12:00: Masataka Chida (Tohoku)
> Beilinson-Flach elements for higher weight modular forms.
>
> 13:30-14:30: Kazim Buyukboduk
> Exceptional zeros of p-non-ordinary forms and Perrin-Riou's conjecture - II
>
> 15:00-16:30: Fabien Trihan (Tokyo)
> Geometric Iwasawa Main and Equivariant Tamagawa Number Conjectures - II
>
>
> ABSTRACTS
>
> Exceptional zeros of p-non-ordinary forms and Perrin-Riou's conjecture
> (Buyukboduk):
>
> I will report on a joint work with Denis Benois where we prove a p-adic
> Beilinson formula for the second derivative of the p-adic L-function
> associated to a newform f which is non-crystalline semistable at p, at its
> central critical point, by expressing this quantity in terms of a p-adic
> (cyclotomic) regulator defined on an extended trianguline Selmer group. We
> also prove a two-variable version of this result for height pairings we
> construct by considering infinitesimal deformations afforded by a Coleman
> family passing through f. This, among other things, leads us to a proof of
> a version of Perrin-Riou's conjecture in this set up, allowing us to relate
> Heegner cycles on appropriately chosen Shimura curves to Beilinson-Kato
> elements.
>
>
> Selmer groups and the central values of L-functions for modular forms
> (Chida):
>
> In this talk, we will discuss on a relation between the order of Selmer
> groups and the central values of Rankin-Selberg L-functions associated to
> modular forms and finite order Hecke characters. In particular, we will
> show that the non-vanishing of the central L-value implies the finiteness
> of Selmer groups under mild assumptions, which is expected by Bloch-Kato's
> Tamagawa number conjecture. This is a generalization of results by
> Bertolini-Darmon and Longo-Vigni to higher weight modular forms. The proof
> uses a Kolyvagin system constructed from CM cycles on Kuga-Sato varieties
> over Shimura curves.
>
>
> Beilinson-Flach elements for higher weight modular forms (Chida):
>
> This is a joint work with François Brunault. In this talk, we will
> construct an element in higher K-groups of the product of two Kuga-Sato
> varieties. This gives a generalization of Beilinson-Flach elements to
> higher weight modular forms. Also we will introduce an explicit formula for
> the image of the element under the regulator map. This result is related to
> Beilinson's conjecture on non-critical values of Rankin-Selberg L-functions
> for modular forms.
>
>
> Geometric Iwasawa Main and Equivariant Tamagawa Number
> Conjectures (Trihan):
>
> Let A/K be an abelian variety over a function field of characteristic p>0.
> We will give a survey on recent results concerning the Iwasawa Main and ETN
> conjectures in this context.
>
>
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