Project description

Our aim is threefold. The basic objects are non-proper Shimura varieties (embeddable in the Siegel space), automorphic bundles, their various Chern classes over compactifications of the Shimura varieties. The goals:1) Construct Chern classes of automorphic vector bundles in l-adic cohomology of the minimal compactification of a Shimura variety over barQ.2) Try to understand in which more arithmetic cohomology it is possible to lift those l-adic Chern classes.3) If 1) and 2) were available, one could try to construct the l-adic realization of the motivic mixed Tate extensions which are believed by many people to exist.

Related publications

Published articles

Hélène Esnault, A. Shiho, Chern classes of crystals,Transactions of the AMS 371 2 (2019), 1333-1358.

Hélène Esnault, T. Abe, A Lefschetz theorem for overconvergent isocrystals with Frobenius structure, Annales de l'École Normale Supérieure, 52 (4) (2019), 1243--1264.

Giulio Brescani, Some implications between Grothendieck's anabelian conjectures, Algebraic Geometry, vol.8, issue 2.

Giulio Brescani, Essential dimension and pro-finite group schemes, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), XXII (2021) no. 4, 1899-1936.

Giulio Brescani, On the section conjecture and Brauer-Severi varieties, Mathematische Zeitschrift, 300 (2022) no.2, 1291-1296.

Preprints

Giulio Brescani, On the section conjecture over fields of finite type, arxiv:1911.03234

Giulio Brescani, A. Vistoli, An elementary approach to Stix's proof of the real section conjecture, arxiv:2012.06278

Giulio Brescani, On the Bombieri-Lang Conjecture over finitely generated fields. arxiv:2012.15765.

Giulio Brescani, A higher dimensional Hilbert irreducibility theorem. arxiv:2101.01090

Giulio Brescani, On the birational section conjecture with strong birationality assumptions. arxiv:2108.13397.

Giulio Brescani, A. Vistoli, The genericity theorem for the essential dimension of tame stacks. arxiv:2111.01117.