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Accueil > Agenda > Colloques et rencontres > Archives > Agenda 2019 > Dijon-Freiburg-Strasbourg Joint Seminar

Dijon-Freiburg-Strasbourg Joint Seminar

IRMA, May 16th 2019

The "Joint Seminar" is a research seminar in Arithmetic and Algebraic Geometry, organized by the research groups in Dijon, Freiburg, and Strasbourg. The seminar meets roughly once per semester in Strasbourg, for a full day. There are about three talks per meeting, both by invited guests and by speakers from the organizing universities. We aim to leave ample room for discussions and for a friendly chat.

Organizers : Giuseppe Ancona (Strasbourg), Frédéric Déglise (Dijon) and Annette Huber (Freiburg)

The talks are open for everyone. Contact one of the organizers if you are interested in attending the meeting. We have some (very limited) funds that might help to support travel for some junior participants.

The seminar will meet in Strasbourg, Mayl 16th 2019 in the conference room of the institute.

8h45 - coffee

9h15 - Daniele Faenzi (Dijon) : Fano threefolds of genus 10 and Coble cubics

abstract : The moduli space of Fano threefolds of genus 10 is a tenfold that maps onto the moduli space of genus-2 curves via the period map. I will describe the fibre of this map as an open dense subset of the dual of the Coble cubic in P8.
10h20 - coffee

11h - Brad Drew (Freiburg) : A universal property of Ayoub’s six-functor formalism

Abstract : The stable motivic homotopy category SH(S) over a scheme S is characterized by an ∞-categorical universal property : each homology theory on the category of smooth S-schemes satisfying algebraic analogues of the Eilenberg-Steenrod axioms factors essentially uniquely through SH(S). Ayoub has equipped the categories SH(S) with a six-functor formalism, i.e., pullback, pushforward, and tensor operations satisfying the same formal properties as derived categories of ℓ-adic sheaves. In this talk, we will promote the universal property of SH(S) to a universal property of the associated six-functor formalism : each six-functor formalism S ↦ D(S) satisfying a reasonable list of axioms admits an essentially unique family of functors SH(S) → D(S) compatible with the six operations. As an application, we construct various motivic realization functors.
12h20 - Lunch at MiTo

14h30 - Mattia Cavicchi (Paris 13) : Weights of the boundary motive of genus 2 Hilbert-Siegel varieties

Let S be a Shimura variety of abelian type, associated to a reductive group G. Each algebraic representation V of G gives rise to a mixed sheaf \mu(V) on S (both in the Hodge-theoretic and in the l-adic sense). When S is non-compact, the weight filtrations on the cohomology of \mu(V), and on the cohomology of its degeneration at the boundary of a compactification of S, carry important arithmetic information. In this talk, we will look at the case of G=GSp_4/F (for F a totally real number field), corresponding to genus 2 Hilbert-Siegel varieties, and we will explain how to characterize the presence of certain weights in terms of an invariant of irreducible representations of G, called corank. In particular, thanks to Wildeshaus’ theory, this description allows one to construct, in many cases, homological motives associated to cuspidal automorphic representations of G.

Dernière mise à jour le 16-05-2019