Project C7: Automorphic representations and their local factors
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
Henri Johnston, Andreas Nickel PDF
On the $p$-adic Stark conjecture at $s=1$ and applications
Project:
C7
X
On the $p$-adic Stark conjecture at $s=1$ and applications
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17001
Nils Ellerbrock, Andreas Nickel PDF
On Formal Groups and Tate Cohomology in Local Fields
Project:
C7
X
On Formal Groups and Tate Cohomology in Local Fields
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15041
Henri Johnston, Andreas Nickel PDF
On the non-abelian Brumer–Stark conjecture
Project:
C7
X
On the non-abelian Brumer–Stark conjecture
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15026
Felix Bergunde, Lennart Gehrmann PDF
On the order of vanishing of Stickelberger elements of Hilbert modular forms
Project:
C7
X
On the order of vanishing of Stickelberger elements of Hilbert modular forms
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14046
Henri Johnston, Andreas Nickel PDF
Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture
Project:
C7
X
Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture
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13002
Werner Hoffmann PDF
Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups
Project:
C7
X
Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups
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13001
Werner Hoffmann, Satoshi Wakatsuki PDF
On the geometric side of the Arthur trace formula for the symplectic group of rank 2
Project:
C7
X
On the geometric side of the Arthur trace formula for the symplectic group of rank 2
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12126
Henri Johnston, Andreas Nickel PDF
On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results
Project:
C7
X
On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results
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12056
Werner Hoffmann PDF
Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups
Project:
C7
X
Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups
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12018
Michael Spieß PDF
Shintani cocycles and vanishing order of p-adic Hecke L-series at s = 0
Project:
C7
X
Shintani cocycles and vanishing order of p-adic Hecke L-series at s = 0
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