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SUMMARY:Motives\, quadratic forms and arithmetic
DTSTART;VALUE=DATE-TIME:20221024T060000Z
DTEND;VALUE=DATE-TIME:20221028T150000Z
DTSTAMP;VALUE=DATE-TIME:20230326T015200Z
UID:indico-event-6044@indico.math.cnrs.fr
DESCRIPTION:\n\n24-28 October 2022 in Lens\, France\n\nTheme\n\nMotives we
re originally introduced by Grothendieck in the sixties to provide a unive
rsal source to various cohomology theories of algebraic\, geometric and ar
ithmetic nature.\n\nThe works of Hanamura\, Levine and Voevodsky in the ni
neties\, followed by many others\, have shed a new light on the subject by
introducing triangulated categories of motives and relating them to a new
ly defined homotopy category of schemes. More recent avatars of motives in
clude the motives with modulus of Kahn\, Miyazaki\, Saito and Yamazaki or
the log-motives of Binda\, Park and Østvær\, both purposely avoiding A1-
invariance.\n\nMotivic methods have also pervaded arithmetic geometry\, wh
ich is the use of methods of algebraic geometry over a base of arithmetic
nature such as a number field\, in order to study number theoretical probl
ems such as Diophantine equations. Several famous unresolved conjectures p
redict general patterns and guide mathematicians in the area\, among which
Grothendieck's standard conjectures\, the Hodge conjecture(s)\, the Tate
conjecture and the Beilinson conjecture.\n\nThe remaining theme of this co
nference\, quadratic forms\, is a subject in its own right. The algebraic
theory of quadratic forms over fields has bloomed in the last fifty years\
, with tremendous progress in the computations of their discrete invariant
s. The connexion with motives goes both ways: the understanding of the mot
ives of geometric objects related to quadratic forms\, such as quadrics\,
has been the source of many beautiful results on quadratic forms\, while i
n reverse\, invariants of quadratic nature\, such as Hermitian K-theory or
Chow-Witt groups somewhat surprisingly appear in the endomorphisms of the
motivic 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 Fe
derico 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 Ja
vier Fresán (Palaiseau)\n \n \n Florian Ivorra (Rennes)\n \n \n Moritz Ke
rz (Regensburg)\n \n \n Florence Lecomte (Strasbourg)\n \n \n Marc Levine
(Essen)\n \n \n Hiroyasu Miyazaki (Tokyo)\n \n \n Alena Pirutka (New-York\
, Paris)\n \n \n Joël Riou (Orsay)\n \n \n Sujatha (Vancouver)\n \n \n C
laire Voisin (Paris)\n \n \n Olivier Wittenberg (Villetaneuse)\n \n \n Tak
ao Yamazaki (Sendai)\n \n\n\nOrganizers / Organisateurs\n\nJérôme Burés
i\, Baptiste Calmès\, Ivo Dell'Ambrogio\, Ahmed Laghribi\n\nScientific Co
mmittee / Comité scientifique\n\nYves André\, Anna Cadoret\, Shuji Saito
\n\n \n\n \n\n \n\n \n\n \n\nhttps://indico.math.cnrs
.fr/event/6044/
LOCATION:Louvre Lens Vallée
URL:https://indico.math.cnrs.fr/event/6044/
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