No abstract uploaded!

We calculate the local Fourier transforms for connections on the formal punctured disk, reproducing the results of J. Fang and C. Sabbah using a different method. Our method is similar to Fang’s, but more direct.

We make the elementary observation that the Lagrangian submanifolds of$C$^{$n$},$n$≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov–Eliashberg algebra is acyclic.

No abstract uploaded!

Abstract We present a relative trace formula approach to the Gross–Zagier formula and its generalization to higher-dimensional unitary Shimura vari- eties. As a crucial ingredient, we formulate a conjectural arithmetic funda- mental lemma for unitary Rapoport–Zink spaces. We prove the conjecture when the Rapoport–Zink space is associated to a unitary group in two or three variables.