Third meeting
Time: November 21, 2015.
Venue: Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research
Speakers:
Kento Fujita (Kyoto University), Yoshinori Gongyo (University of Tokyo), Shenghao Sun (Yau Mathematical Sciences Center) and Jean-Louis Colliot-Thélène (Université Paris-Sud)
Schedule:
9:30-10:00 coffee
10:00-11:00 Yoshinori Gongyo: Rational points on log Fano threefolds over a finite field
Abstract: We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, a klt Fano threefold over a finite field has a rational point. This is a joint work with Yusuke Nakamura and Hiromu Tanaka.
11:30-12:30 Jean-Louis Colliot-Thélène: Chow group of cycles of codimension two and third unramified cohomology
Abstract: Algebraic K-theory provides relations between the third unramified cohomology group (with torsion coefficients) of a smooth projective variety and the Chow group of codimension 2 cycles. This is used to study the image of such cycles under various cycle class maps into integral cohomogy. It is also used to investigate rationality questions for Fano hypersurfaces and for homogeneous spaces of connected linear algebraic groups. There are many open questions.
14:00-15:00 Shenghao Sun: Decomposition theorem and Independence of \ell
Abstract: The BBDG Decomposition theorem says that, over any algebraically closed base field, the \ell-adic intersection complex on an algebraic variety is taken to a direct sum of semisimple perverse sheaves, appropriately shifted in the derived category, under proper pushforwards. Each simple summand in the decomposition has a support by definition, and it is natural to expect that these supports remain unchanged as we vary the auxiliary choice of the prime \ell. We sketch the proof in the case when the base field is the algebraic closure of a finite field.
15:00-15:30 coffee
15:30-16:30 Kento Fujita: Optimal bounds for the volumes of Kahler-Einstein Fano manifolds
Abstract: We show that any $n$-dimensional Kahler-Einstein Fano manifold $X$ satisfies that the anti-canonical volume is less than or equal to the value $(n+1)^n$. Moreover, the equality holds if and only if $X$ is isomorphic to the projective space.
Organizers
Baohua Fu, Wenfei Liu, Xiaotao Sun, Chenyang Xu
Contact
Ms. Meng Yu
No. 78 Jingchunyuan, Peking University,
Beijing, China 100871
Tel.: +(86 10) 6274 4121