A FROBENIUS QUESTION RELATED TO ACTIONS ON CURVES IN CHARACTERISTIC P
نویسندگان
چکیده
منابع مشابه
A Frobenius Question Related to Actions on Curves in Characteristic P
We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases. Required Publisher's Statement This article was p...
متن کاملGonality of modular curves in characteristic p
Let k be an algebraically closed field of characteristic p. Let X(p;N) be the curve parameterizing elliptic curves with full level N structure (where p N) and full level p Igusa structure. By modular curve, we mean a quotient of any X(p;N) by any subgroup of ((Z/peZ)× × SL2(Z/NZ)) /{±1}. We prove that in any sequence of distinct modular curves over k, the k-gonality tends to infinity. This exte...
متن کاملCANONICAL HEIGHTS ON ELLIPTIC CURVES IN CHARACTERISTIC p
Let k = Fq(t) be the rational function field with finite constant field and characteristic p ≥ 3, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curveE/K which has ordinary reduction at all places ofK extending v, we consider a canonical height pairing 〈 , 〉v : E(K ) × E(K) → C v which is symmetric, bilinear and Galois equivariant. The pairing 〈 , 〉∞ for t...
متن کاملLimit Linear Series in Positive Characteristic and Frobenius-Unstable Vector Bundles on Curves
Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of P1 with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. We also develop a new, more functorial construction for the basic theory of limit linear series, which works transparently in posi...
متن کاملOn a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristic p
It is known that the Grauert-Riemenschneider vanishing theorem is not valid in characteristic p ([1]). Here we show that it may be restored in the presence of a suitable Frobenius splitting. The proof uses interchanging two projective limits, one involving iterated Frobenius maps, cf. [2] and [4], the other coming from Grothendieck’s theorem on formal functions. That leads to the following gene...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2013
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089513000128