中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
华罗庚青年数学论坛报告
Speaker: Dr. Ruofan Jiang (UC Berkeley)
Inviter: 余红杰
Language: English
Title: Mumford-Tate conjecture and unlikely intersection in char p
Time & Venue: 2026年8月20日（星期四） 14:15-15:15 MCM110
Abstract: For an abelian variety A over a number field, the Mumford-Tate group MT(A) is the monodromy group of its Hodge structure. It is conjectured that MT(A) tensor Q_p is the neutral component of the p-adic étale monodromy group G_p(A). I will talk about an analogue of the conjecture in char p, and show that it is equivalent to an unlikely intersection problem of Ax-Lindemann type. Time permitting, I will talk about one of the following two topics: André-Oort conjecture in char p, or p-adic Hodge loci.
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Speaker: Dr. Ruofan Jiang (UC Berkeley)
Inviter: 余红杰
Language: English
Title: Integral cycles on reductions of K3 surfaces
Time & Venue: 2026年8月20日（星期四） 15:30-16:30 MCM110
Abstract: I give an application of mod p Mumford-Tate in the last talk: Given an ordinary K3 surface X over a char p global field K, we show that for an arbitrary infinite collection M of positive integers coprime to p, there are infinitely many places of K modulo which the reduction of X has an extra line bundle of self-intersection number lying in M. The main input is an algebraization result established via mod p Mumford-Tate for Spin Shimura varieties, which reduces us to a situation where we apply Diophantine approximation to the Picard group. This is a forthcoming joint work with Ananth Shankar.
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