Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project C7

## Automorphic representations and their local factors

Principal Investigator(s) Other Investigators

## Summary:

The fine geometric expansion of the Arthur-Selberg trace formula, which is a prerequisite for the global Jacquet-Langlands correspondence, shall be reformulated in a way that is valid in positive characteristic too. We will study smooth representations of $GL_n(F)$, with $F$ a $p$-adic field, on $F_p$-vector spaces. We aim to generalise a representation theoretic construction which is available for $n=2$ to arbitrary $n$. Periods of cuspidal automorphic representations of $GL_2$ and its inner forms at places of "split multiplicative type" shall be defined and their functorial properties and relations to $p$-adic $L$-functions and periods of $p$-adic Galois representations shall be studied.

## Recent Preprints:

 13002 Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups PDF | PS.GZ 13001 On the geometric side of the Arthur trace formula for the symplectic group of rank 2 PDF | PS.GZ 12126 On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results PDF | PS.GZ 12056 Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups PDF | PS.GZ 12018 Shintani cocycles and vanishing order of p-adic Hecke L-series at s = 0 PDF | PS.GZ 12007 The kernel of Ribet’s isogeny for genus three Shimura curves PDF | PS.GZ 12006 Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes PDF | PS.GZ