Lifting automorphisms on Abelian varieties as derived autoequivalences

Groups of Autoequivalences of Derived Categories of Smooth Projective Varieties

Linear criteria for lifting automorphisms of elementary abelian regular coverings

For a given finite connected graph , a group H of automorphisms of and a finite group A, a natural question can be raised as follows: Find all the connected regular coverings of having A as its covering transformation group, on which each automorphism in H can be lifted. In this paper, we investigate the regular coverings with A = Zp , an elementary abelian group and get some new matrix-theoret...

Linear bound for abelian automorphisms of varieties of general type (

The aim of this paper is to prove the following Theorem 1. Let G be a finite abelian group acting faithfully on a complex smooth project variety X of general type with numerically effective (nef) canonical divisor, of dimension n. Then |G| ≤ C(n)K n X , where C(n) depends only on n. We refer to the Introduction of [Ca-Sch] for a nice account of the history for the study of bounds of automorphis...

Lifting systems of Galois representations associated to abelian varieties

This paper treats what we call ‘weak geometric liftings’ of Galois representations associated to abelian varieties. This notion can be seen as a generalization of the idea of lifting a Galois representation along an isogeny of algebraic groups. The weaker notion only takes into account an isogeny of the derived groups and disregards the centres of the groups in question. The weakly lifted repre...

Exceptional Sequences and Derived Autoequivalences

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y admitting a full exceptional sequence. Applications include the case in which X is Calabi-Yau and either X is a hypersurface in Y (this extends a previous result b...