Title: Arithmetic D-modules and existence of "petits camarades cristallins"
Abstract: In this talk, we show the existence of crystalline companion of l-adic smooth sheaf on curves. For this, we need a six functor formalism which includes the rigid cohomology theory. This formalism was proposed by P. Berthelot in 80's, but we need to wait till Kedlaya proved semistable reduction theorem for overconvergent isocrystals before we finally get fundamental theorems for the theory due mostly to D. Caro. We show the theorem by extending the formalism to certain stacks and by using the strategy of Drinfeld and Lafforgue on the establishment of Langlands correspondence.
Enlin Yang (Berlin)
Title: On the semi-continuity of total dimension divisor
Abstract: This is a joint work with Haoyu Hu. We prove an inequality for the pullback of total dimension divisors of étale sheaves on a smooth scheme over an algebraically closed field of positive characteristic. We also prove a lower semi-continuity property for total dimension in higher relative dimension under some assumptions. The proofs are based on the semi-continuity property of Swan conductor which is due to Deligne and Laumon.
Adrian Langer (Warsaw)
Title: Rigid rank 3 representations of the fundamental group
Wataru Kai (Tokyo)
Title: A moving lemma for algebraic cycles with modulus and contravariance
Abstract: The theory of algebraic cycles with modulus, such as the additive higher Chow group introduced by Bloch and Esnault and the higher Chow group with modulus by Binda, Kerz and Saito, is an emerging branch of algebraic cycle theory. The concept "modulus" concerns how cycles behave at the boundary, expressed by a Cartier divisor. In this talk we exhibit how the contravariance (in affine smooth varieties) of these theories can be deduced from a “moving lemma with modulus.” We explain what new aspects are added by the modulus condition when establishing it.
Marta Pieropan (Berlin)
Title: Torsors, Cox rings and Manin's conjecture
Abstract: A conjecture of Manin predicts an asymptotic formula for the distribution of rational points on Fano varieties over number fields. I will present recent parameterization techniques, involving torsors under quasitori and a new notion of Cox rings, that are used to verify the asymptotic formula for some families of varieties.
Sinan Ünver (Berlin/Istanbul)
Title: On the algebra of p-adic multi-zeta values
Abstract: p-adic multi-zeta values are the p-adic periods of the unipotent fundamental group of the thrice punctures line. They turn out to give all the p-adic periods of mixed Tate motives over Z. In this talk we will give an explicit series representation of these values in all depths. The new tool is a certain regularization trick for p-adic series.
Phung Ho Hai (Hanoi)
Title: Tannakian duality over dedekind rings and applications
Fabio Tonini (Berlin)
Valentina Di Proietto (Berlin)
Matthias Schuett (Hannover)
Title: Lines on smooth quartics in IP^3
Abstract: Starting from the classical 27 lines on smooth cubic surfaces in IP^3, I will discuss the problem how many lines a smooth quartic may contain. The talk will review Segre’s seminal ideas (over the complex numbers) and blend them with the modern approach through elliptic fibrations, aiming for a complete picture in any characteristic. Special emphasis will be put on the critical case of characteristic 2. For most part, this is joint work with Slawomir Rams (Krakow).