Zero estimates on group varieties II

Cryptography on Trace-Zero Varieties

Residues and Zero-Cycles on Algebraic Varieties

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Zero-cycles on varieties over finite fields

For any field k, Milnor [Mi] defined a sequence of groups K 0 (k), K M 1 (k), K M 2 (k), . . . which later came to be known as Milnor K-groups. These were studied extensively by Bass and Tate [BT], Suslin [Su], Kato [Ka1], [Ka2] and others. In [Som], Somekawa investigates a generalization of this definition proposed by Kato: given semi-abelian varieties G1, . . . , Gs over a field k, there is a...

Group Actions on Jacobian Varieties

Consider a finite groupG acting on a Riemann surface S, and the associated branched Galois cover πG : S → Y = S/G. We introduce the concept of geometric signature for the action of G, and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group G acting on the Jacobian varie...

Group Actions on Quiver Varieties and Applications

We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we construct branes in hyperkähler quiver varieties, as fixed loci of such actions.