2 results
Common valuations of division polynomials
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 26 February 2024, pp. 1-15
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In this note, we prove a formula for the cancellation exponent $k_{v,n}$
between division polynomials $\psi _n$
and $\phi _n$
associated with a sequence $\{nP\}_{n\in \mathbb {N}}$
of points on an elliptic curve $E$
defined over a discrete valuation field $K$
. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.
Bökstedt periodicity and quotients of DVRs
- Part of
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 8 / August 2022
- Published online by Cambridge University Press:
- 27 September 2022, pp. 1683-1712
- Print publication:
- August 2022
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In this paper we compute the topological Hochschild homology of quotients of discrete valuation rings (DVRs). Along the way we give a short argument for Bökstedt periodicity and generalizations over various other bases. Our strategy also gives a very efficient way to redo the computations of
$\operatorname {THH}$ (respectively, logarithmic 
$\operatorname {THH}$) of complete DVRs originally due to Lindenstrauss and Madsen (respectively, Hesselholt and Madsen).
