Ignazio Longhi

E-MAIL：Ignazio.Longhi@xjtlu.edu.cn

Deparment: School of Science

Items: 7

Views: 193

1. An example of non-cotorsion Selmer group

Author:Lai,King Fai;Longhi,Ignazio;Tan,Ki Seng;Trihan,Fabien

Source:Proceedings of the American Mathematical Society,2015,Vol.143

Abstract:Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.

2. Characteristic ideals and Iwasawa theory

Author:Bandini, A;Bars, F;Longhi, I

Source:NEW YORK JOURNAL OF MATHEMATICS,2014,Vol.20

Abstract:Let Lambda be a nonnoetherian Krull domain which is the inverse limit of noetherian Krull domains Lambda(d) and let M be a finitely generated A-module which is the inverse limit of Lambda(d)-modules M-d. Under certain hypotheses on the rings Lambda(d) and on the modules M-d, we define a procharacteristic ideal for M in Lambda, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a nonnoetherian Iwasawa algebra Z(p)[[Gal(F/F)]], where F is a function field of characteristic p and Gal(F/F) similar or equal to Z(p)(infinity).

3. PONTRYAGIN DUALITY FOR IWASAWA MODULES AND ABELIAN VARIETIES

Author:Lai, KF;Longhi, I;Tan, KS;Trihan, F

Source:TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2018,Vol.370

Abstract:We prove a functional equation for two projective systems of finite abelian p-groups, {a,} and {60, endowed with an action of 4 such that a, can be identified with the Pontryagin dual of 6 for all n. Let K be a global field. Let L be a 4-extension of K (d > 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.

4. The Iwasawa Main Conjecture for constant ordinary abelian varieties over function fields

Author:Lai, KF;Longhi, I;Tan, KS;Trihan, F

Source:PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY,2016,Vol.112

Abstract:We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over Z(p)(d)-extensions of function fields ramifying at a finite set of places.

5. The Iwasawa Main Conjecture for semistable abelian varieties over function fields

Author:Lai, KF;Longhi, I;Tan, KS;Trihan, F

Source:MATHEMATISCHE ZEITSCHRIFT,2016,Vol.282

Abstract:We prove the Iwasawa Main Conjecture over the arithmetic -extension for semistable abelian varieties over function fields of characteristic .

6. Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

Author:Angles, B;Bandini, A;Bars, F;Longhi, I

Source:MATHEMATISCHE ANNALEN,2020,Vol.376

Abstract:We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field F-q (theta) (p is a prime of F-q [theta]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero-Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers beta(j) (i.e., on the values of the Carlitz-Goss zeta-function at negative integers).

7. Characteristic ideals and Selmer groups

Author:Bandini, A;Bars, F;Longhi, I

Source:JOURNAL OF NUMBER THEORY,2015,Vol.157

Abstract:Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a Z(p)(N)-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a procharacteristic ideal associated to the Pontrjagin dual of the p-primary Selmer group of A. To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Z(p)(d)-extension F-d/F and for any Z(p)(d-1)-extension contained in F-d, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z(p)[[Gal(F/F)]] in the case A is a constant abelian variety. (C) 2015 Elsevier Inc. All rights reserved.

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