Welcome to the 2025
Fall talks of ODTÜ-Bilkent Algebraic Geometry
Seminars
since 2000
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This week the ODTÜ-Bilkent Algebraic Geometry Seminar is online
This talk will begin at 15:40 (GMT+3)
Please check your time difference between Ankara and your city here
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This week the ODTÜ-Bilkent Algebraic Geometry Seminar is online
This talk will begin at 15:40 (GMT+3)
Please check your time difference between Ankara and your city here
=================================================================
Gustave Boulanger (1824-1888)
Title:
Euler systems for
exterior square motives
Abstract:
The Birch–Swinnerton-Dyer
conjecture relates the behavior of the
L-function of an elliptic curve at its central
point to the rank of its group of rational
points. The Bloch–Kato conjecture generalizes
this principle to a broad family of motivic
Galois representations, predicting a precise
relationship between the order of vanishing of
motivic L-functions at integer values and the
structure of the associated Selmer groups. Since
the foundational work of Kolyvagin in the
nineties, Euler systems have played a central
role in approaching these conjectures, and in
recent years their scope has expanded
significantly within the automorphic setting of
Shimura varieties.
In this talk, I will focus on unitary Shimura varieties GU(2,2), whose middle-degree cohomology realizes the exterior square of the four-dimensional Galois representations attached to certain automorphic representations of GL_4. The period integral formula of Pollack–Shah for exterior square L-functions has a natural motivic interpretation, suggesting the feasibility of constructing a nontrivial Euler system. A key obstacle to this construction is the failure of a suitable multiplicity-one property, which has long prevented the verification of the certain norm relations required for Euler system methods. I will present a new approach that overcomes this difficulty. The resulting Euler system in the middle-degree cohomology of GU(2,2) provides the first nontrivial evidence toward the Bloch–Kato conjecture for exterior square motives and opens several promising avenues for further arithmetic applications. This is joint work with Andrew Graham and Antonio Cauchi.
In this talk, I will focus on unitary Shimura varieties GU(2,2), whose middle-degree cohomology realizes the exterior square of the four-dimensional Galois representations attached to certain automorphic representations of GL_4. The period integral formula of Pollack–Shah for exterior square L-functions has a natural motivic interpretation, suggesting the feasibility of constructing a nontrivial Euler system. A key obstacle to this construction is the failure of a suitable multiplicity-one property, which has long prevented the verification of the certain norm relations required for Euler system methods. I will present a new approach that overcomes this difficulty. The resulting Euler system in the middle-degree cohomology of GU(2,2) provides the first nontrivial evidence toward the Bloch–Kato conjecture for exterior square motives and opens several promising avenues for further arithmetic applications. This is joint work with Andrew Graham and Antonio Cauchi.
Date: 28 November 2025,
Friday
Time: 15:40 (GMT+3)
Place: Zoom
Place: Zoom
Participants who have registered will receive the Zoom link via email one day before the seminar.
If you registered for a previous talk in this series, there's no need to register again—you'll automatically receive the link for this session.
If you haven't registered yet, please contact sertoz@bilkent.edu.tr to be added to the mailing list.
You are most cordially invited to
attend.
Ali Sinan Sertöz
This seminar series is
organized by a joint team from ODTÜ and
Bilkent
Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
---------------------------------------------------------------------------- Ali Sinan Sertöz Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye Office: (90)-(312) - 290 1490 Department: (90)-(312) - 266 4377 e-mail: sertoz@bilkent.edu.tr Web: sertoz.bilkent.edu.tr ----------------------------------------------------------------------------