5 papers
Horizontal norm compatibility of cohomology classes for
Syed Waqar Ali Shah
We establish abstract horizontal norm relations involving the unramified Hecke-Frobenius polynomials that correspond under the Satake isomorhpism to the degree eight spinor -fac…
On constructing zeta elements for Shimura varieties
Syed Waqar Ali Shah
We present a novel axiomatic framework for establishing horizontal norm relations in Euler systems that are built from pushforwards of classes in the motivic cohomology of Shimura…
Norm relations for CM points on modular curves
Syed Waqar Ali Shah
Kolyvagin introduced the method of Euler systems to study the structure of Selmer groups of elliptic curves. In this semi-expository article, we prove the horizontal norm relations…
Explicit Hecke descent for special cycles
Syed Waqar Ali Shah
We derive an explicit formula for the action of a geometric Hecke correspondence on special cycles on a Shimura variety in terms of such cycles at a fixed neat level and compare it…
On distribution relations of polylogarithmic Eisenstein classes
Syed Waqar Ali Shah
We show that for Siegel modular varieties of arbitrary genus, the natural distribution relations satisfied by certain integral Eisenstein cohomology classes defined by Kings admit…