Rationally connected varieties over finite fields
نویسندگان
چکیده
منابع مشابه
2 Rationally Connected Varieties over Finite Fields
In this paper we study rationally connected varieties defined over finite fields. Then we lift these results to rationally connected varieties over local fields. Roughly speaking, a variety X over an algebraically closed field is rationally connected if it contains a rational curve through any number of assigned points P1, . . . , Pn. See [Kollár01a] for an introduction to their theory and for ...
متن کاملRationally Connected Varieties over Finite Fields
Let X be a geometrically rational (or, more generally, separably rationally connected) variety over a finite field K . We prove that if K is large enough, then X contains many rational curves defined over K . As a consequence we prove that R-equivalence is trivial on X if K is large enough. These results imply the following conjecture of J.L. Colliot-Thélène: Let Y be a rationally connected var...
متن کاملRationally Connected Varieties over Finite Fields János Kollár
In this paper we study rationally connected varieties defined over finite fields. Then we lift these results to rationally connected varieties over local fields. Roughly speaking, a variety X over an algebraically closed field is rationally connected if it contains a rational curve through any number of assigned points P1, . . . , Pn. See [Kollár01] for an introduction to their theory and for a...
متن کاملRationally Connected Varieties over Local Fields
LetX be a proper variety defined over a fieldK. Following [Manin72], two points x, x ∈ X(K) are called R-equivalent if they can be connected by a chain of rational curves defined over K, cf. (4.1). In essence, two points are R-equivalent if they are “obviously” rationally equivalent. Several authors have proved finiteness results over local and global fields (cubic hypersurfaces [Manin72, Swinn...
متن کاملRATIONALLY CONNECTED VARIETIES OVER LOCAL FIELDS 359 Conjecture
Let X be a proper variety defined over a field K. Following [Ma], we say that two points x, x′ ∈ X(K) are R-equivalent if they can be connected by a chain of rational curves defined over K (cf. (4.1)). In essence, two points are R-equivalent if they are “obviously” rationally equivalent. Several authors have proved finiteness results over local and global fields (cubic hypersurfaces [Ma], [SD],...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2003
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-03-12022-0