Stephen S. Kudla Department of Mathematics University of Toronto 40 St. George St., BA6290 Toronto, ON M5S 2E4 Canada

This lead to some of the problems studied below. In particular, the conservation conjecture stated above and its analogue for unitary groups were found by the first author while visiting the Tata Institute in …

Here we mention only the work of Dihua Jiang, [9], who ⊗ ⊗ gave an intriguing relation with a period of an Eisenstein series on G2 and the recent Princeton thesis of Thomas Watson, [26], who applies …

The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry. At the moment, no general theory of such …

10. On a conjecture of Jacquet, (joint with Michael Harris), in Contributions to Automorphic Forms, Geometry and Arithmetic, H. Hida, D. Ramakrishnan, and F. Shahidi, eds., Johns Hopkins Press, …

At this point, I am going to give an idealized picture which ignores many serious technical problems involving: (i) the existence of good integral models, (ii) bad reduction and the possible bad behavior …

There are many technical problems which must be overcome to obtain such results. For example, one would like to work with a model over Spec (Z). If V is anisotropic, then M is projective, but if V is …

Abstract We prove a relation between a generating series for the heights of Heegner cycles on the arithmetic surface associated to a Shimura curve and the second term in the Laurent expansion at s …

Zp . The above proposition tells us that, when K = Kp Kp , as above, then · MKp provides us with a smooth model of Sh(G, D)K over Z(p) . From now on, we will use the same notation for both moduli …

It seems to us that our results on degenerate special cycles constitute only the beginning of a circle of very interesting problems. This also explains the di erent and much more open-ended nature of this …