Zero-cycles on varieties over $p$-adic fields and Brauer groups
نویسندگان
چکیده
منابع مشابه
ZERO-CYCLES ON VARIETIES OVER p-ADIC FIELDS AND BRAUER GROUPS
In this paper, we study the Brauer-Manin pairing of smooth proper varieties over local fields, and determine the p-adic part of the kernel of one side. We also compute the A0 of a potentially rational surface which splits over a wildly ramified extension.
متن کاملFINITENESS THEOREM ON ZERO-CYCLES OVER p-ADIC FIELDS
Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 11 3. Vanishing theorem 15 4. Bertini theorem over a discrete valuation ring 19 5. Surjectivity of cycle map 22 6. Blowup formula 24 7. A moving lemma 26 8. Proof of main theorem 28 9. Applications of main theorem 31 Appendix A. Resolution of singularities for embedded curves 34 References 39
متن کاملZero-cycles on varieties over finite fields
For any field k, Milnor [Mi] defined a sequence of groups K 0 (k), K M 1 (k), K M 2 (k), . . . which later came to be known as Milnor K-groups. These were studied extensively by Bass and Tate [BT], Suslin [Su], Kato [Ka1], [Ka2] and others. In [Som], Somekawa investigates a generalization of this definition proposed by Kato: given semi-abelian varieties G1, . . . , Gs over a field k, there is a...
متن کاملA FINITENESS THEOREM FOR ZERO-CYCLES OVER p-ADIC FIELDS
Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 12 3. Vanishing theorem 16 4. Bertini theorem over a discrete valuation ring 20 5. Surjectivity of cycle map 23 6. Blow-up formula 25 7. A moving lemma 28 8. Proof of main theorem 30 9. Applications of main theorem 33 Appendix A.
متن کاملBRAUER-TYPE RESULTS ON SEMIGROUPS OVER p-ADIC FIELDS
In this paper we consider the following problem. Let k < K be fields. Suppose S ⊂ Mn(K) is an absolutely irreducible multiplicative semigroup with the property that the spectrum of every a ∈ S is contained in k. Does it follow that S is simultaneously realizable in Mn(k), that is, does there exist a p ∈ GLn(K) such that pSp−1 ⊂ Mn(k)? The overfield K plays no essential role in this situation. C...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2014
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2220