Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Project C7

Automorphic representations and their local factors


Principal Investigator(s) Other Investigators
Werner Hoffmann
Andreas Nickel
Michael Spieß
Felix Bergunde
Chuangxun Cheng
Lennart Gehrmann
Thomas Jahn
Jeanine van Order

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:

17006 On the $p$-adic Stark conjecture at $s=1$ and applications PDF | PS.GZ
17001 On Formal Groups and Tate Cohomology in Local Fields PDF | PS.GZ
15041 On the non-abelian Brumer–Stark conjecture PDF | PS.GZ
15026 On the order of vanishing of Stickelberger elements of Hilbert modular forms PDF | PS.GZ
14046 Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture PDF | PS.GZ
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