Publications (5)
The -motivic Gysin map
Longke Tang
We develop a -unstable non--invariant theory of motivic spaces and spectra, and construct the Gysin map therein for regular immersions. This in particul…
Syntomic cycle classes and prismatic Poincaré duality
Longke Tang
We introduce -gauges over a prism, construct syntomic cycle classes, and prove the prismatic Poincaré duality for proper smooth schemes.
Slicing criterion for ind-smooth ring maps
Longke Tang
We show that ind-smoothness of flat ring maps can be tested on constructible stratifications, even for maps of non-Noetherian rings. We prove this by generalizing ind-smoothness an…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
On the Standard Lattices
Rongquan Feng, Longke Tang, Kun Wang
A lattice in the Euclidean space is standard if it has a basis consisting vectors whose norms equal to the length in its successive minima. In this paper, it is shown that with the…