Abstract
We study the connection between the singularities of a finite type ℤ-scheme X and the asymptotic point count of X over various finite rings. In particular, if the generic fiber Xℚ = X xSpecℤ Specℚ is a local complete intersection, we show that the boundedness of |X(ℤ/pnℤ)|/pndimX ℚ in p and n is in fact equivalent to the condition that Xℚ is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.
Original language | English (US) |
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Pages (from-to) | 485-500 |
Number of pages | 16 |
Journal | Algebra and Number Theory |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2 2019 |
Funding
I would like to thank my advisor Avraham Aizenbud for presenting me with this problem, teaching and helping me in this work. I hold many thanks to Nir Avni for helpful discussions and for hosting me at Northwestern University in July 2016, during which a large part of this work was done. I also thank Yotam Hendel for fruitful talks. This work was partially supported by the ISF grant [687/13], the BSF grant [2012247] and the Minerva Foundation grant.
Keywords
- Analysis on p-adic varieties
- Asymptotic point count
- Complete intersection
- Rational singularities
ASJC Scopus subject areas
- Algebra and Number Theory