RANK ONE CONNECTIONS ON ABELIAN VARIETIES, II

Rank One Eisenstein Cohomology of Local Systems on the Moduli Space of Abelian Varieties

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations.

Indices of Rank and of Singularity on Abelian Varieties.

I G. W. Ford and G. E. Uhlenbeck, "Combinatorial Problems in the Theory of Graphs. I," these PROCEEDINGS, 42, 122, 1956; G. W. Ford, B. Z. Norman, and G, E. Uhlenbeck, "Combinatorial Problems in the Theory of Graphs. II," these PROCEEDINGS, 42, 203, 1956; G. W. Ford and G. E. Uhlenbeck, "Combinatorial Problems in the Theory of Graphs. III," these PROCEEDINGS, 42, 529, 1956. We shall refer to th...

On the Rank of Abelian Varieties over Function Fields

Let C be a smooth projective curve defined over a number field k, A/k(C) an abelian variety and (τ, B) the k(C)/k-trace of A. We estimate how the rank of A(k(C))/τB(k) varies when we take a finite Galois k-cover π : C → C defined over k.

The Rank One Abelian Stark Conjecture

Regularity on abelian varieties

I will introduce the notion of Mukai regularity for coherent sheaves on abelian varieties, defined via conditions on the supports of the cohomologies of Fourier-Mukai transform complexes. In a very special form, depending on the choice of a polarization, this resembles and in fact strenghtens the classical notion of Castelnuovo-Mumford regularity. The techniques are in part a generalization of ...