scholarly journals Tate modules of isocrystals and good reduction of Drinfeld modules

2021 ◽  
Vol 15 (4) ◽  
pp. 909-970
Author(s):  
Max (Maxim) Mornev
Keyword(s):  
Drinfeld Modules ◽  
Good Reduction

GAUSSIAN LAWS ON DRINFELD MODULES

2009 ◽  
Vol 05 (07) ◽  
pp. 1179-1203 ◽  
Author(s):  
WENTANG KUO ◽  
YU-RU LIU
Keyword(s):  
Finite Field ◽  
Polynomial Ring ◽  
Valuation Ring ◽  
Finite Extension ◽  
Drinfeld Modules ◽  
Good Reduction ◽  
Prime Divisors ◽  
Frobenius Automorphism ◽  
Tate Module ◽  
Rank 2

Let A = 𝔽q[T] be the polynomial ring over the finite field 𝔽q, k = 𝔽q(T) the rational function field, and K a finite extension of k. Let ϕ be a Drinfeld A-module over K of rank r. For a place 𝔓 of K of good reduction, write [Formula: see text], where [Formula: see text] is the valuation ring of 𝔓 and [Formula: see text] its maximal ideal. Let P𝔓, ϕ(X) be the characteristic polynomial of the Frobenius automorphism of 𝔽𝔓acting on a Tate module of ϕ. Let χϕ(𝔓) = P𝔓, ϕ(1), and let ν(χϕ(𝔓)) be the number of distinct primes dividing χϕ(𝔓). If ϕ is of rank 2 with [Formula: see text], we prove that there exists a normal distribution for the quantity [Formula: see text] For r ≥ 3, we show that the same result holds under the open image conjecture for Drinfeld modules. We also study the number of distinct prime divisors of the trace of the Frobenius automorphism of 𝔽𝔓acting on a Tate module of ϕ and obtain similar results.

Cryptanalysis of a cryptosystem based on Drinfeld modules

2006 ◽  
Vol 153 (1) ◽  
pp. 12
Author(s):  
S.R. Blackburn ◽  
C.F.A. Cid ◽  
S.D. Galbraith
Keyword(s):  
Drinfeld Modules

scholarly journals Cogalois theory and drinfeld modules

2019 ◽  
Vol 19 (01) ◽  
pp. 2050001
Author(s):  
Marco Antonio Sánchez–Mirafuentes ◽  
Julio Cesar Salas–Torres ◽  
Gabriel Villa–Salvador
Keyword(s):  
Class Number ◽  
Present Form ◽  
Drinfeld Modules ◽  
Carlitz Module ◽  
Rank One

In this paper, we generalize the results of [M. Sánchez-Mirafuentes and G. Villa–Salvador, Radical extensions for the Carlitz module, J. Algebra 398 (2014) 284–302] to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension [Formula: see text].

scholarly journals RAPOPORT–ZINK UNIFORMIZATION OF HODGE-TYPE SHIMURA VARIETIES

2018 ◽  
Vol 6 ◽  
Author(s):  
WANSU KIM
Keyword(s):  
Shimura Varieties ◽  
Good Reduction ◽  
Canonical Models

We show that the integral canonical models of Hodge-type Shimura varieties at odd good reduction primes admits ‘$p$-adic uniformization’ by Rapoport–Zink spaces of Hodge type constructed in Kim [Forum Math. Sigma6(2018) e8, 110 MR 3812116].

scholarly journals Torsion points of elliptic curves with good reduction

2008 ◽  
Vol 31 (3) ◽  
pp. 385-403
Author(s):  
Masaya Yasuda
Keyword(s):  
Elliptic Curves ◽  
Good Reduction ◽  
Torsion Points

Relative Yetter-Drinfeld modules and comodules over braided groups

2015 ◽  
Vol 56 (4) ◽  
pp. 041706 ◽  
Author(s):  
Haixing Zhu
Keyword(s):  
Drinfeld Modules
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