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- W4200428244 abstract "In the paper (J Math Soc Jpn 72(1):303–331, 2020), Tse-Chung Yang and the first two current authors computed explicitly the number $$|mathrm {SSp}_2(mathbb {F}_q)|$$ of isomorphism classes of superspecial abelian surfaces over an arbitrary finite field $$mathbb {F}_q$$ of even degree over the prime field $$mathbb {F}_p$$ . There it was assumed that certain commutative $$mathbb {Z}_p$$ -orders satisfy an étale condition that excludes the primes $$p=2, 3, 5$$ . We treat these remaining primes in the present paper, where the computations are more involved because of the ramification. This completes the calculation of $$|mathrm {SSp}_2(mathbb {F}_q)|$$ in the even degree case. The odd degree case was previous treated by Tse-Chung Yang and the first two current authors in (Doc Math 21:1607–1643, 2016). To complete the proof of our main theorem, we give a classification of lattices over local quaternion Bass orders, which is a new input to our previous works." @default.
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- W4200428244 date "2021-12-14" @default.
- W4200428244 modified "2023-10-16" @default.
- W4200428244 title "On Superspecial abelian surfaces over finite fields III" @default.
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- W4200428244 doi "https://doi.org/10.1007/s40993-021-00303-8" @default.
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