The HUJI-BGU Workshop in Arithmetic
The HUJI-BGU Workshop in Arithmetic meets twice a semester,
alternating locations, starting from the year 5780. All are
The workshop is currently organized by Ari Shnidman
(HUJI) and Daniel
1st meeting: Monday December 16th, 2019 -
The day will be dedicated to the memory of John Tate, who passed
away on October 16th, 2019. Tate's
ideas "have dominated the development of arithmetic algebraic
geometry" (from the 2003 Wolf Prize citation).
10.30 - 11.00 (Manchester, Faculty lounge) Welcome
11.00 - 11:45 (Ross 63) Shay Ben Moshe (HUJI), Tate elliptic
curves and p-adic uniformization
12.00 - 13.00 (Ross 63) Ariel Weiss (HUJI), l-adic Tate
modules and good reduction
13.00 - 14.00 (Manchester, Faculty lounge) Lunch
14.00 - 15:30 (Ross 70) David Jarossay (BGU), p-adic Tate
modules and good reduction
Abstracts of talks
Shay Ben Moshe (11:00-11:45)
We start by considering elliptic curves over the complex numbers.
They admit analytic uniformization, namely they are given as a
quotient of the complex plane by a lattice. This allows us to draw
many conclusions about them, for example understand their torsion.
We then try to mimic this in the p-adic situation. We
describe a family of p-adic elliptic curves, the Tate
elliptic curves, and sketch a proof that they admit p-adic
uniformization. We apply this to give some structural results about
them, such as describing the Galois action on their Tate module
Ariel Weiss (12:00-13:00)
If E is an elliptic curve over a number field K, then, by a deep
conjecture of Tate (now a theorem of Faltings), E is determined up
to isogeny by its l-adic Tate module. In particular, any
isogeny invariant of E should be encoded in its Tate module. In this
expository talk, we study the criterion of
N\'eron--Ogg--Shafarevich, which states that E has good reduction at
a prime of K that is coprime to l if and only if its l-adic
Tate module is unramified.
We will begin by reviewing the arithmetic theory of elliptic curves
and their Tate modules, before stating the N\'eron--Ogg--Shafarevich
criterion, sketching its proof and giving several examples and
David Jarossay (14.00-15.30)
This talk will be about a paper by Coleman and Iovita, which
shows two descriptions of a filtered Frobenius monodromy module
attached to the H^1_dR of elliptic curves (more generally
Abelian varieties) with split semistable reduction over Q_p. The
equivalence between the two descriptions is induced by Colmez's
p-adic integration pairing. A corollary is that, for A an
Abelian variety over a local field, the p-adic Tate module of A
is crystalline if and only if A has good reduction.
Dates to be saved
2nd meeting: January 13th, 2020 - BGU
HUJI: Einstein Institute of Mathematics, Hebrew University
Giv'at Ram Campus, Jerusalem.
BGU: Deichmann Building for Mathematics, Ben-Gurion University of
the Negev, Be'er Sheva.
Directions: you may use Google Maps or Moovit. (Please note that
Google is sometimes optimistic about the travel time of local