Sommaire du Fascicule no. 1

Two monoidal structures on Satake category in mixed characteristic
Katsuyuki Bando
p. 1-25
Kida’s formula for split prime $\mathbb{Z}_p$-extensions over imaginary quadratic fields
Kazuaki Murakami
p. 27-55
Bertrand’s and Rodriguez Villegas’ conjecture for real multi-quadratic Galois extensions of the rationals
Dohyeong Kim ; Seungho Song
p. 57-69
Primes with small primitive roots
Kevin Ford ; Mikhail R. Gabdullin ; Andrew Granville
p. 71-89
Additive Ramsey theory over Piatetski-Shapiro numbers
Jonathan Chapman ; Sam Chow ; Philippa Holdridge
p. 91-110
Determination of certain mod $p$ Galois representations using local constancy
Abhik Ganguli ; Suneel Kumar
p. 111-161
A note on the factorization of iterated quadratics over finite fields
Vefa Goksel
p. 163-178
More on consecutive multiplicatively dependent triples of integers
Michael A. Bennett ; István Pink ; Ingrid Vukusic
p. 179-222
Multi-height analysis of rational points of toric varieties
Nicolas Bongiorno
p. 223-252
Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials
Nobuo Tsuzuki ; Takuya Yamauchi
p. 253-293
On Grothendieck’s section conjecture for curves of index $1$
Giulio Bresciani
p. 295-316