that the mathematical literature as a whole is so reliable comes down to the fact that, over time, we have made an even number of sign errors
Daniel Litt
@littmath.bsky.social
5.9K followers 285 following 766 posts
Assistant professor (of mathematics) at the University of Toronto. Algebraic geometry, number theory, forever distracted and confused, etc. He/him.
![General remarks
Following the terminology of [A04b], this question asks for a computation of the "Frobenius amplitude" of an ample vector bundle in positive characteristic. The notion is motivated by the algebraic proof of Kodaira vanishing in [DI87], due to Raynaud.
The main result of [A04b] shows that, given 𝑋 in characteristic zero, ℰ be an ample vector bundle on 𝑋 and 𝒢 a coherent sheaf on 𝑋, there exists a spreading out of the data (𝑋,ℰ,𝒢) such that modulo almost all primes, the vanishing in the problem statement holds. In positive characteristic, the desired vanishing is only known under strong liftability assumptions [L19], namely that rk(ℰ) <char(𝑘), and that 𝑋 admits a lift
˜
𝑋
to 𝑊2(𝑘) such that ℰ(𝑝𝑁) lifts to
˜
𝑋
for some 𝑁 >0. While this yields some pleasant applications the hypotheses are likely not optimal.
Formalizability
I am not sure if this statement can be formalized given the current state of MathLib.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:wvexgwndckqyszwviyuoeibi/bafkreicdljvmqfhm4cfffcb73y3guprhes3w5kmq6ojhgtt4b7wavsmdo4)
