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Department of Mathematical Sciences

# Research Seminar Series

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.

## Arithmetic Study Group: The p-adic Stark conjecture at s=1 and applications

Presented by Henri Johnston, University of Exeter

21 November 2017 14:00 in CM 219

Let E/F be a finite Galois extension of totally real number fields and
let p be a prime. The `p-adic Stark conjecture at s=1' relates the
leading terms at s=1 of p-adic Artin L-functions to those of the
complex Artin L-functions attached to E/F. When E=F this is equivalent
to Leopoldt’s conjecture for E at p and the ‘p-adic class number
formula’ of Colmez. In this talk we discuss the p-adic Stark
conjecture at s=1 and applications to certain cases of the equivariant
Tamagawa number conjecture (ETNC). This is joint work with
Andreas Nickel.