Motives Today
Hotel Villa Madruzzo,
Cognola (Trento), Italy
June 3.rd-7.th,
2019
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MUSE - Archivio APT Trento – Foto Hufton & Crow |
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Scientific Organizers |
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Format
and speakers |
This school consists
of three courses (of about 6 hours each, to be spread on five days) delivered
by:
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Program:
titles and abstracts of the courses |
Click here to see the
program. Giuseppe Ancona: Motives over finite fields and over the
complex numbers We will discuss
examples where questions on algebraic cycles are easier over the complex
numbers and others which are easier over finite
fields. We will try to give intuitions on the differences between these two
situations. A preliminary list of results we will treat is
the following: the Kunneth conjecture for varieties
over finite fields (Katz-Messing 1973), the Bloch Beilinson
conjecture for elliptic curves over finite fields (Kahn 2002 and Jannsen 2007), standard conjectures for complex abelian
varieties (Kleiman 1968 and Lieberman 1968),
partial results on standard conjectures for abelian varieties over finite
fields (Clozel 1999 and Ancona 2018). Robert Laterveer: Motives and non-rationality In the first half, I
intend to give a gentle introduction to algebraic
cycles, Chow groups and the various categories of pure motives. In the second
half, I will give an overview of results of the last few years concerning
non-rationality of certain families of algebraic varieties (Voisin, Totaro, Colliot-Thelene-Pirutka, …). These results rely on Chow-theoretic techniques, in
particular the notion of “integral decomposition of the diagonal”. Charles Vial: Weight decompositions for Chow motives Some 25 years ago,
Jacob Murre introduced the notion of Chow-Kuenneth decomposition, or weight decomposition, for Chow
motives and conjectured that the motive of every smooth projective variety
admits such a decomposition, and also conjectured
how such decompositions should behave. I will start by explaining the link
between Murre’s conjectures, the existence of a
conjectural Bloch-Beilinson filtration on the Chow
ring of smooth projective varieties, Kimura’s finite-dimensionality
conjecture, and the conservativity conjecture.
After reviewing examples of varieties for which a weight decomposition does
exist, I will more specifically focus on the case of abelian varieties, where
weight decompositions with further structures exist (compatibility with the
intersection product). Finally, I will suggest that the motives of hyperKaehler varieties admit similar weight
decompositions as that of abelian varieties. |
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Confirmed
Participants |
Click here to see the
list. |
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Registration
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For registering in the school please complete and submit our registration
form to the Secretary of CIRM. Young researchers are encouraged to
participate. It is possible to support the full board and lodging in a shared
double bedroom at the hotel to some of them upon request. Unfortunately, it
is not possible to reimbourse travel expenses.
People interested in having such a support should send a short CV to the
Secretary of CIRM together with the registration form. No registration fee will be charged. Deadline for
registration: April 15, 2019. |
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Logistic Information |
The school will be held in the conference hall of the Hotel Villa Madruzzo in Cognola (Trento).
Participants will be lodged in the same hotel.
Arrival day is Sunday, June 2nd in the afternoon/evening. Lectures
will start in the morning of Monday, June 3rd and end at lunchtime of Friday, June
7th . Departure day is Friday, June 7th after lunch. The cost for the
full board and lodging at the Hotel Villa Madruzzo
is:
Please click here to find Information to reach the Hotel Villa Madruzzo. |
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Sponsors
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