We define push-forwards along projective morphisms in the Witt theory of smooth quasi-projective varieties over a field. We prove that they have standard properties such as functoriality, compatibility with pull-backs and projection formulas.

Tetsushi Ito (Kyoto University, Graduate School of Science, Assistant Professor) 【Outline of survey】 Shimura varieties are algebraic varieties (geometric objects defined by equations), which are generalizations of modular curves. Previously, several mathematical objects in arithmetic geometry, Galois representations, automorphic representations were studied from individual perspectives. However...

We study the action of endomorphisms of a Drinfeld A-module φ on its de Rham cohomology HDR(φ,L) and related modules, in the case where φ is defined over a field L of finite Acharacteristic p. Among others, we find that the nilspace H0 of the total Frobenius FrDR on HDR(φ,L) has dimension h = height of φ. We define and study a pairing between the p-torsion pφ of φ and HDR(φ,L), which becomes pe...

We show how the classical moving lemma of Chow extends to give functoriality for the specta arising in the homotopy coniveau tower.

The recent construction of Siegel modular forms of degree 2n from elliptic cusp forms by Ikeda is interpreted as a special case of Langlands functoriality. This is then used to express the (full) spin L–function of an Ikeda lift as a product of symmetric power L–functions for GL(2). As a corollary one obtains the desired analytic properties of these spin L–functions provided the analogous prope...