1. Multiplier ideal sheaves with weights of Lelong number one
Speaker(s): GUAN Qi'an, Peking University
Venue: Room 29, Quan Zhai, BICMR
Time: 10:10am-12:00pm, Tuesday, Oct. 13th
The title is: Multiplier ideal sheaves with weights of Lelong number one
Abstract: In this talk, we present our characterization of multiplier ideal sheaves with weights of Lelong number one, which depends on our solution of Demailly's strong openness conjecture. We also present a new proof of the related well known integrability criterion due to Skoda. This is joint work with Professor Xiangyu Zhou.
2. Perfectoid Shimura varieties of abelian type
Speaker(s): Xu Shen (申旭), Morningside center of Mathematics, AMSS.
Venue: Quan 9
Time：10/13 4PM-6PM
Title: Perfectoid Shimura varieties of abelian type.
Abstract: We prove that Shimura varieties of abelian type with infinite level at p are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with infinite level at p are also perfectoid.
3. The Brauer group of schemes
Speaker(s): Jean-Louis Colliot-Thelene (CNRS & Universite Paris Sud)
Venue: 教208
Time: Nov. 3, 10, 17, 24 3:10-6:00
Summary:
The Brauer group of algebraic varieties features prominently in at least two directions of research: birational problems (the L¨uroth problem) and arithmetic geometry (Brauer-Manin obstruction).
The November 2015 lectures will be devoted to the algebraic theory of the Brauer
group. The first part will be devoted to the general properties of the Brauer group.
The second part will be concerned with concrete computations of the Brauer group for various classes of algebraic varieties.
References:
J-P. Serre, Cohomologie galoisienne, Lecture Notes in Mathematics, vol. 5, 5`eme ´edition, r´evis´ee, Springer-Verlag 1994. Translated into English as “Galois cohomology”, Springer monographes in Mathematics,1997.
A. Grothendieck, Le groupe de Brauer I, II, III, in Dix expos´es sur la cohomologie des sch´emas, Masson and North Holland, 1968.
Le groupe de Brauer : I. Alg`ebres d’Azumaya et interpr´etations diverses.
S´eminaire Bourbaki, 9 (1964-1966), Expos´e No. 290, available on NUMDAM,
search :http://www.numdam.org/numdam-bin/qrech
Also : https://eudml.org/doc/109691
Le groupe de Brauer : II. Th´eories cohomologiques. S´eminaire Bourbaki,
9 (1964-1966), Expos´e No. 297, available on NUMDAM, use :
http://www.numdam.org/numdam-bin/qrech
Also :
https://eudml.org/doc/109698
The three talks GBI, GBII, GBIII, are available in the whole volume “Dix expos´es
sur la cohomologie des sch´emas ” available at:
webusers.imj-prg.fr/∼leila.schneps/grothendieckcircle/DixExp.pdf
J. S. Milne, Etale Cohomology, Princeton University Press, 1980. Chapters 1 to 4.
P. Gille and T. Szamuely, Central simple algebras and Galois cohomology, Cambridge
studies in advanced mathematics 101 (2006). Chapters 1 to 6.
J.-L. Colliot-Th´el`ene et J.-J. Sansuc, The rationality problem for fields of
invariants under linear algebraic groups, Proceedings of the International Colloquium
on Algebraic groups and Homogeneous Spaces (Mumbai 2004), ed. V. Mehta, TIFR Mumbai,
Narosa Publishing House (2007), 113–186.
http://www.math.u-psud.fr/∼colliot/mumbai04.pdf
J.-L. Colliot-Th´el`ene, Notes on the Brauer group
http://www.math.u-psud.fr/∼colliot/CTnotesBrauer.pdf