TY - JOUR
T1 - On rational singularities and counting points of schemes over finite rings
AU - Glazer, Itay
N1 - Funding Information:
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.
Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.
PY - 2019/3/2
Y1 - 2019/3/2
N2 - 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 X ℚ = X xSpecℤ Specℚ is a local complete intersection, we show that the boundedness of |X(ℤ/p n ℤ)|/p ndimX ℚ in p and n is in fact equivalent to the condition that X ℚ is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.
AB - 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 X ℚ = X xSpecℤ Specℚ is a local complete intersection, we show that the boundedness of |X(ℤ/p n ℤ)|/p ndimX ℚ in p and n is in fact equivalent to the condition that X ℚ is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.
KW - Analysis on p-adic varieties
KW - Asymptotic point count
KW - Complete intersection
KW - Rational singularities
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U2 - 10.2140/ant.2019.13.485
DO - 10.2140/ant.2019.13.485
M3 - Article
AN - SCOPUS:85065229176
VL - 13
SP - 485
EP - 500
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 2
ER -