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SUMMARY:Motives\, quadratic forms and arithmetic
DTSTART;VALUE=DATE-TIME:20221024T060000Z
DTEND;VALUE=DATE-TIME:20221028T150000Z
DTSTAMP;VALUE=DATE-TIME:20211023T205500Z
UID:indico-event-6044@indico.math.cnrs.fr
DESCRIPTION:\n\n*** Update (August 28th\, 2021) ***\n\nThe conference ha
s been rescheduled to 24-28th of October *2022*\n\nTheme\n\nMotives were
originally introduced by Grothendieck in the sixties to provide a universa
l source to various cohomology theories of algebraic\, geometric and arith
metic nature.\n\nThe works of Hanamura\, Levine and Voevodsky in the ninet
ies\, followed by many others\, have shed a new light on the subject by in
troducing triangulated categories of motives and relating them to a newly
defined homotopy category of schemes. More recent avatars of motives inclu
de the motives with modulus of Kahn\, Miyazaki\, Saito and Yamazaki or the
log-motives of Binda\, Park and Østvær\, both purposely avoiding A1-inv
ariance.\n\nMotivic methods have also pervaded arithmetic geometry\, which
is the use of methods of algebraic geometry over a base of arithmetic nat
ure such as a number field\, in order to study number theoretical problems
such as Diophantine equations. Several famous unresolved conjectures pred
ict general patterns and guide mathematicians in the area\, among which Gr
othendieck's standard conjectures\, the Hodge conjecture(s)\, the Tate con
jecture and the Beilinson conjecture.\n\nThe remaining theme of this confe
rence\, quadratic forms\, is a subject in its own right. The algebraic the
ory of quadratic forms over fields has bloomed in the last fifty years\, w
ith tremendous progress in the computations of their discrete invariants.
The connexion with motives goes both ways: the understanding of the motive
s of geometric objects related to quadratic forms\, such as quadrics\, has
been the source of many beautiful results on quadratic forms\, while in r
everse\, invariants of quadratic nature\, such as Hermitian K-theory or Ch
ow-Witt groups somewhat surprisingly appear in the endomorphisms of the mo
tivic stable homotopy category of schemes.\n\nSpeakers / Orateurs\n\n\n \n
Luca Barbieri-Viale (Milan)\n \n \n Olivier Benoist (Paris)\n \n \n Feder
ico Binda (Milan)\n \n \n Jean-Louis Colliot-Thélène (Orsay) \n \n \n
Frédéric Déglise (Lyon)\n \n \n Hélène Esnault (Berlin)\n \n \n Flori
an Ivorra (Rennes)\n \n \n Moritz Kerz (Regensburg)\n \n \n Florence Lecom
te (Strasbourg)\n \n \n Marc Levine (Essen)\n \n \n Hiroyasu Miyazaki (Tak
ao)\n \n \n Alena Pirutka (New-York\, Paris)\n \n \n Joël Riou (Orsay)\n
\n \n Sujatha (Vancouver)\n \n \n Claire Voisin (Paris)\n \n \n Olivier W
ittenberg (Villetaneuse)\n \n \n Takao Yamazaki (Sendai)\n \n\n\nOrganizer
s / Organisateurs\n\nJérôme Burési\, Baptiste Calmès\, Ivo Dell'Ambrog
io\, Ahmed Laghribi\n\nScientific Committee / Comité scientifique\n\nYves
André\, Anna Cadoret\, Shuji Saito\n\n \nhttps://indico.math.cnrs.fr/ev
ent/6044/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6044/
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