8 papers
Localization and elliptic motivic relations
Peter Xu
We observe that the motivic analogue of Suslin reciprocity (and similar degree-zero statements) is a formal consequence of localization (plus purity/some six functor formalism). In…
Presenting restricted Steinberg modules of general linear groups
Peter Xu
We give generators and presentations for various local restrictions of Steinberg modules over fields and relate them to \emph{partial} Borel--Serre compactifications of locally sym…
A note on polyhedral cones and toric polylogarithms
Peter Xu
We extend some methods of our previous work on special elements in Milnor K-theory of algebraic tori, exhibiting in particular a -equivariant isomorphism…
A note on cubical Bloch--Levine cycle complexes
Peter Xu
We check that Levine's simplicial--cubical comparison argument for Bloch's cycle complexes also works over an arbitrary DVR. As a result, the sheaf of cubical Bloch cycle complexes…
Eisenstein class of a torus bundle and log-rigid analytic classes for
Martí Roset, Peter Xu
Starting from a topological treatment of the Eisenstein class of a torus bundle, we define log-rigid analytic classes for . These are group cohomology cl…
Explicit formula for the theta lift via Bruhat decomposition
Peter Xu
Using combinations of weight-1 and weight-2 of Kronecker-Eisenstein series to construct currents in the distributional de Rham complex of a squared elliptic curve, we find a simple…
Classical periods of Eisenstein series and Bernoulli polynomials in the equivariant cohomology of a torus
Peter Xu
We find group cochains valued in currents giving explicit representatives for the -equivariant polylogarithm class of a torus. Based on the construction of weight-…
Symbols for toric Eisenstein cocycles and arithmetic applications
Peter Xu
Using a complex parameterizing rational spherical chains, we construct explicit cocycles for $\mathrm{GL}_n(\Q)$ valued in the motivic cohomology of (open subsets of) the algebraic…