2 results
On even K-groups over p-adic Lie extensions of global function fields
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 22 January 2025, pp. 1-15
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Let p be a fixed prime number, and let F be a global function field with characteristic not equal to p. In this article, we shall study the variation properties of the Sylow p-subgroups of the even K-groups in a p-adic Lie extension of F. When the p-adic Lie extension is assumed to contain the cyclotomic
$\mathbb {Z}_p$-extension of F, we obtain growth estimate of these groups. We also establish a duality between the direct limit and inverse limit of the even K-groups.
Growth of
$\unicode[STIX]{x0428}$ in towers for isogenous curves
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 11 / November 2015
- Published online by Cambridge University Press:
- 30 June 2015, pp. 1981-2005
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- November 2015
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We study the growth of
$\unicode[STIX]{x0428}$ and 
$p^{\infty }$-Selmer groups for isogenous abelian varieties in towers of number fields, with an emphasis on elliptic curves. The growth types are usually exponential, as in the ‘positive 
${\it\mu}$-invariant’ setting in the Iwasawa theory of elliptic curves. The towers we consider are 
$p$-adic and 
$l$-adic Lie extensions for 
$l\neq p$, in particular cyclotomic and other 
$\mathbb{Z}_{l}$-extensions.
