21 research outputs found
Statistics for Iwasawa invariants of elliptic curves, II
We study the average behavior of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants
-invariant stability in families of modular Galois representations
Consider a family of modular forms of weight 2, all of whose residual
Galois representations are isomorphic. It is well-known that their
corresponding Iwasawa -invariants may vary. In this paper, we study
this variation from a quantitative perspective, providing lower bounds on the
frequency with which these -invariants grow or remain stable.Comment: final version; to appear in Research in the Mathematical Science
Statistics for Iwasawa Invariants of elliptic curves,
We study the average behaviour of the Iwasawa invariants for Selmer groups of
elliptic curves. These results lie at the intersection of arithmetic statistics
and Iwasawa theory. We obtain unconditional lower bounds for the density of
rational elliptic curves with prescribed Iwasawa invariants.Comment: 23 pages, minor changes. Accepted for publication in the
International Journal of number theor
Heuristics for anti-cyclotomic -extensions
This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this
by proposing two heuristics supported by computations. First we propose the
Intersection Heuristics: these model `how often' the -Hilbert class field of
an imaginary quadratic field intersects the anti-cyclotomic tower and to what
extent. Second we propose the Invariants Heuristics: these predict that the
Iwasawa invariants and usually vanish for imaginary quadratic
fields where is non-split.Comment: v2: Incorporated changes as per the referee reports; accepted for
publication (Experimental Math
Studying Hilbert's 10th problem via explicit elliptic curves
N.Garc\'ia-Fritz and H.Pasten showed that Hilbert's 10th problem is
unsolvable in the ring of integers of number fields of the form
for positive proportions of primes and
. We improve their proportions and extend their results to the case of
number fields of the form , where
belongs to an explicit family of positive square-free integers. We achieve this
by using multiple elliptic curves, and replace their Iwasawa theory arguments
by a more direct method.Comment: Comments very welcome
Structure of fine Selmer groups in abelian p-adic Lie extensions
This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg\u27s Conjecture is clarified
Derived -adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna -adic -function
Let be an elliptic curve and let be an odd prime of good
reduction for . Let be an imaginary quadratic field satisfying the
classical Heegner hypothesis and in which splits. In a previous work,
Agboola--Castella formulated an analogue of the Birch--Swinnerton-Dyer
conjecture for the -adic -function of
Bertolini--Darmon--Prasanna attached to , assuming the prime to be
ordinary for . The goal of this paper is two-fold:
(1) We formulate a -adic BSD conjecture for
for all odd primes of good reduction.
(2) For an algebraic analogue of
, we show that the ``leading coefficient'' part of
our conjecture holds, and that the ``order of vanishing'' part follows from the
expected ``maximal non-degeneracy'' of an anticyclotomic -adic height.
In particular, when the Iwasawa--Greenberg Main Conjecture
is
known, our results determine the leading coefficient of at up to a -adic unit. Moreover, by adapting the approach of
Burungale--Castella--Kim in the -ordinary case, we prove the main conjecture
for supersingular primes under mild hypotheses.Comment: 34 page
STRUCTURE OF FINE SELMER GROUPS IN ABELIAN p-ADIC LIE EXTENSIONS
This paper studies fine Selmer groups of elliptic curves in abelian p-adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Zp-extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified
Efficacy and safety during endoscopic retrograde cholangiopancreatography (ERCP) under total intravenous anesthesia – propofol alone versus propofol supplemented with dexketa, a comparative study in medical college, Kolkata
Background: Endoscopic retrograde cholangiopancreatography (ERCP) is an invasive procedure and, hence, is distressing for awake patients, requiring an adequate level of anesthesia. Recent advancements have encouraged the use of monitored anesthesia care, that allows the patient to tolerate unpleasant experiences during procedures while maintaining cardio-respiratory function. Usually, propofol-based anesthesia is given in ERCP. The main aim of this study is to compare the effect of propofol alone and propofol with ketamine and dexmedetomidine on the hemodynamics during ERCP, recovery profile, and side effects (if any).
Aims and Objectives: (1) To compare efficacy in terms of hemodynamic stability and desaturation events. (2) Recovery and quality of recovery. (3) Pain score. (4) Incidence of post-operative nausea and vomiting.
Materials and Methods: This is a comparative double-blinded study. Adult patients from the age group of 18–70 years belonging to the American Society of Anesthesiologists (ASA-I) and ASA-II who had undergone ERCP under total intravenous anesthesia were taken and randomly assigned to either of the two groups. Both groups received 0.01 mg/kg glycopyrrolate, 0.1 mg/kg ondansetron, 0.05 mg/kg midazolam, 50 mcg fentanyl, and 40 mg hyoscine. Group A patients received 30 mg propofol as a bolus dose and then repeated according to requirements. Group B patients received 0.5 mcg/kg dexmedetomidine as a loading dose and 0.3 mcg/kg/h as a maintenance infusion dose. 30 mg propofol was given before negotiating scope and then 1 mL (1:1) mixture of propofol and ketamine was repeated according to requirements. Total propofol consumption, hemodynamics, quality of recovery, and side effects (if any) were recorded at regular intervals.
Results: The study showed significant cases in Group A had episodes of hypotension and apneic events, whereas there were very few hemodynamic instability and almost no apneic events in Group B patients. The requirement of propofol was much higher in Group A patients.
Conclusion: Dexmedetomidine when used along with propofol and ketamine in ERCP patients reduced the dose requirement of propofol and maintained hemodynamic stability without causing any apneic events