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1 
Some results in Iwasawa Theory and the padic representation theory of padic GL₂Kidwell, Keenan James 25 June 2014 (has links)
This thesis is divided into two parts. In the first, we generalize results of GreenbergVatsal on the behavior of algebraic lambdainvariants of pordinary modular forms under congruence. In the second, we generalize a result of Emerton on maps between locally algebraic parabolically induced representations and unitary Banach space representations of GL₂ over a padic field. / text

2 
Iwasawa theory for elliptic curves with cyclic isogenies /Nichifor, Alexandra. January 2004 (has links)
Thesis (Ph. D.)University of Washington, 2004. / Vita. Includes bibliographical references (p. 5556).

3 
The split prime μconjecture and further topics in Iwasawa theoryCrisan, VladCristian 04 March 2019 (has links)
No description available.

4 
Selmer groups for elliptic curves with isogenies of prime degree /Mailhot, James Michael. January 2003 (has links)
Thesis (Ph. D.)University of Washington, 2003. / Vita. Includes bibliographical references (p. 6568).

5 
A new approach to the investigation of Iwasawa invariantsKleine, Sören 16 December 2014 (has links)
No description available.

6 
Classifying Lambdamodules up to Isomorphism and Applications to Iwasawa TheoryJanuary 2011 (has links)
abstract: In Iwasawa theory, one studies how an arithmetic or geometric object grows as its field of definition varies over certain sequences of number fields. For example, let $F/\mathbb{Q}$ be a finite extension of fields, and let $E:y^2 = x^3 + Ax + B$ with $A,B \in F$ be an elliptic curve. If $F = F_0 \subseteq F_1 \subseteq F_2 \subseteq \cdots F_\infty = \bigcup_{i=0}^\infty F_i$, one may be interested in properties like the ranks and torsion subgroups of the increasing family of curves $E(F_0) \subseteq E(F_1) \subseteq \cdots \subseteq E(F_\infty)$. The main technique for studying this sequence of curves when $\Gal(F_\infty/F)$ has a $p$adic analytic structure is to use the action of $\Gal(F_n/F)$ on $E(F_n)$ and the Galois cohomology groups attached to $E$, i.e. the Selmer and TateShafarevich groups. As $n$ varies, these Galois actions fit into a coherent family, and taking a direct limit one obtains a short exact sequence of modules $$0 \longrightarrow E(F_\infty) \otimes(\mathbb{Q}_p/\mathbb{Z}_p) \longrightarrow \Sel_E(F_\infty)_p \longrightarrow \Sha_E(F_\infty)_p \longrightarrow 0 $$ over the profinite group algebra $\mathbb{Z}_p[[\Gal(F_\infty/F)]]$. When $\Gal(F_\infty/F) \cong \mathbb{Z}_p$, this ring is isomorphic to $\Lambda = \mathbb{Z}_p[[T]]$, and the $\Lambda$module structure of $\Sel_E(F_\infty)_p$ and $\Sha_E(F_\infty)_p$ encode all the information about the curves $E(F_n)$ as $n$ varies. In this dissertation, it will be shown how one can classify certain finitely generated $\Lambda$modules with fixed characteristic polynomial $f(T) \in \mathbb{Z}_p[T]$ up to isomorphism. The results yield explicit generators for each module up to isomorphism. As an application, it is shown how to identify the isomorphism class of $\Sel_E(\mathbb{Q_\infty})_p$ in this explicit form, where $\mathbb{Q}_\infty$ is the cyclotomic $\mathbb{Z}_p$extension of $\mathbb{Q}$, and $E$ is an elliptic curve over $\mathbb{Q}$ with good ordinary reduction at $p$, and possessing the property that $E(\mathbb{Q})$ has no $p$torsion. / Dissertation/Thesis / Ph.D. Mathematics 2011

7 
Noncommutative Iwasawa theory of elliptic curves at primes of multiplicative reductionLee, ChernYang January 2010 (has links)
Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois groupG = Gal(F[infinity]/Q). I show how the p[infinity]Selmer group of E over F[infinity] controls the p[infinity]Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules.

8 
K(1)local Iwasawa theory /Hahn, Rebekah D. January 2003 (has links)
Thesis (Ph. D.)University of Washington, 2003. / Vita. Includes bibliographical references (p. 7980).

9 
On Minimal Levels of Iwasawa TowersJanuary 2013 (has links)
abstract: In 1959, Iwasawa proved that the size of the $p$part of the class groups of a $\mathbb{Z}_p$extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$eigenspace component of the $p$Sylow subgroup of the class group of the field at the $m$th level in a $\mathbb{Z}_p$extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}1,f(T,\omega^{1i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us with a powerful connection between algebraic and analytic techniques; however, as of yet, this isomorphism is unestablished in general. I consider the existence and the properties of an exact sequence $$0\longrightarrow\ker{\longrightarrow}CG_m^i{\longrightarrow}IACG_m^i{\longrightarrow}\textrm{coker}\longrightarrow0.$$ In the case of a $\mathbb{Z}_p$extension where the Main Conjecture is established, there exists a pseudoisomorphism between the respective inverse limits of $CG_m^i$ and $IACG_m^i$. I consider conditions for when such a pseudoisomorphism immediately gives the existence of the desired exact sequence, and I also consider workaround methods that preserve cardinality for otherwise. However, I primarily focus on constructing conditions to verify if a given $m$ is sufficiently large that the kernel and cokernel of the above exact sequence have become wellbehaved, providing similarity of growth both in the size and in the structure of $CG_m^i$ and $IACG_m^i$; as well as conditions to determine if any such $m$ exists. The primary motivating idea is that if $IACG_m^i$ is relatively easy to work with, and if the relationship between $CG_m^i$ and $IACG_m^i$ is understood; then $CG_m^i$ becomes easier to work with. Moreover, while the motivating framework is stated concretely in terms of the cyclotomic $\mathbb{Z}_p$extension of $p$power roots of unity, all results are generally applicable to arbitrary $\mathbb{Z}_p$extensions as they are developed in terms of IwasawaTheoryinspired, yet abstracted, algebraic results on maps between inverse limits. / Dissertation/Thesis / Ph.D. Mathematics 2013

10 
One and TwoVariable $p$adic Measures in Iwasawa TheoryJanuary 2015 (has links)
abstract: In 1984, Sinnott used $p$adic measures on $\mathbb{Z}_p$ to give a new proof of the FerreroWashington Theorem for abelian number fields by realizing $p$adic $L$functions as (essentially) the $Gamma$transform of certain $p$adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$adic $L$functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$adic $L$functions as $Gamma$transforms of certain $p$adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$invariant for certain $mathbb{Z}_p$extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves.
In this thesis, I develop the theory of $p$adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$adic integration, this study includes a strong emphasis on the interpretation of $p$adic measures as $p$adic power series. With this dual perspective, I describe $p$adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$transform on $p$adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudopolynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$transform. I obtain results on the Iwasawainvariants of such pseudopolynomial measures, and use these results to deduce certain continuity results for the $Gamma$transform. As an application, I establish the vanishing of the Iwasawa $mu$invariant of Yager's twovariable $p$adic $L$function from measure theoretic considerations. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2015

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