69,588 research outputs found
Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups
The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over
an algebraically closed field is the least positive integer m such that D[p^m]
determines D up to isomorphism (resp. up to isogeny). We show that these
invariants are lower semicontinuous in families of p-divisible groups of
constant Newton polygon. Thus they allow refinements of Newton polygon strata.
In each isogeny class of p-divisible groups, we determine the maximal value of
isogeny cutoffs and give an upper bound for isomorphism numbers, which is shown
to be optimal in the isoclinic case. In particular, the latter disproves a
conjecture of Traverso. As an application, we answer a question of Zink on the
liftability of an endomorphism of D[p^m] to D.Comment: 50 pages, to appear in Annals of Mathematic
Computing the number of certain Galois representations mod
Using the link between mod Galois representations of \qu and mod
modular forms established by Serre's Conjecture, we compute, for every prime
, a lower bound for the number of isomorphism classes of continuous
Galois representation of \qu on a two--dimensional vector space over \fbar
which are irreducible, odd, and unramified outside .Comment: 28 pages, 3 table
The orbit space of a fusion system is contractible
Given a fusion system F on a finite p-group P, where p is a prime, we show that the partially ordered set of isomorphism classes in F of chains of non-trivial subgroups of P, considered as topological space, is contractible, further generalising Symonds’ proof [19] of a conjecture of Webb [23, 24] and its generalisation to non-trivial Brauer pairs associated with a p-block by Barker [1]
A reciprocity map and the two variable p-adic L-function
For primes p greater than 3, we propose a conjecture that relates the values
of cup products in the Galois cohomology of the maximal unramified outside p
extension of a cyclotomic field on cyclotomic p-units to the values of p-adic
L-functions of cuspidal eigenforms that satisfy mod p congruences with
Eisenstein series. Passing up the cyclotomic and Hida towers, we construct an
isomorphism of certain spaces that allows us to compare the value of a
reciprocity map on a particular norm compatible system of p-units to what is
essentially the two-variable p-adic L-function of Mazur and Kitagawa.Comment: 55 page
A remark on the rank conjecture
We prove a result about the action of -operations on the homology of linear groups. We use this to give a sharper formulation of the rank conjecture as well as some shorter proofs of various known results. We formulate a conjecture about how the sharper formulation of the rank conjecture together with another conjecture could give rise to a different point of view on the isomorphism between and K_n^{(p)} (F)$ for an infinite field F, and we prove part of this new conjecture
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