Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Witt Ring of a Curve with Good Reduction over a Non-dyadic Local Field
252
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals $tilde{I}$ and a sheaf of Witt rings $tilde{W}$ in the obvious way. The Milnor conjecture then relates the associated graded of $tilde{W}$ to Milnor K-theory and so allows the classical invariants of a bilinear space over a field to be extended to our setting using etale cohomology. As an application of these results, we calculate the Witt ring of a smooth curve with good reduction over a non-dyadic local field.
rate research
Read More
In this paper we calculate the Witt ring W(C) of a smooth geometrically connected projective curve C over a finite field of characteristic different from 2. We view W(C) as a subring of W(k(C)) where k(C) is the function field of C. We show that the triviality of the Clifford algebra of a bilinear space over C gives the main relation. The calculation is then completed using classical results for bilinear spaces over fields.
The rings of $p$-typical Witt vectors are interpreted as spaces of vanishing cycles for some perverse sheaves over a disc. This allows to localize an isomorphism emerging in Drinfelds theory of prismatization [Dr], Prop. 3.5.1, namely to express it as an integral of a standard exact triangle on the disc.
For a local complete intersection morphism, we establish fiberwise denseness in the $n$-dimensional irreducible components of the compactification Nisnevich locally.
We provide a simple approach for the crystalline comparison of Ainf-cohomology, and reprove the comparison between crystalline and p-adic etale cohomology for formal schemes in the case of good reduction.
Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined, and an application to a question of Ihara is discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
